Wild Theory.

[Kindler]

Bob did know.  He compartmentalized the knowledge.  He created a new personality for dealing with Harry.  One that did not know that Justin was Kemmler.  This new personality became the Bob we all know and love due to Harry's ability to alter the nature of things by Naming them.  After the battle and Harry became the skull's master, Evil Bob got pushed fully into the background and Bob became the dominant personality, still never knowing that Justin was Kemmler.

I've often wondered about Bob's personality. In Ghost Story, Bob claims that first impressions are really important, which is why he's mostly the same with Butters as he was with Harry. So either A) Harry picked up a random skull and imprinted his 16-year-old personality on Bob, or B) Harry knew what Bob was, which means he had a previous sense of Bob's personality (because I'd imagine he would've had to have seen Bob in action in some fashion), which is why he picked up the skull after his fight with Justin, which means that Harry's original impression of Bob shaped a chunk of, if not all, of his personality. If A is true, then whatever, Bob is Bob because of Harry, but if B is true, then Bob might've been greatly similar to the way he is now under Justin, which says a lot about Justin's personality.

There is, in my opinion, a third option: Justin had a standing order for Bob to lop off his Kemmler personality in the event of his death, which created enough of a blank slate that Harry's personality impacted Bob more than Butters's.

[Lost Merlin]

I think that bob via butters is so similar to bob via harry is because butters knew of bob while he was with harry still.  Butters as the owner formed and impression of how bob was to be based on his previous interactions of bob via harry.  This is why I think that Bob has not changed much, other then the fun new Jewish Phrases. 

[exartiem]

I think it is a gradual thing.  The longer Bob is with Butters, the more like Butters he's going to become.  I think is might have been more rapid with young Harry because Bob was more of a blank slate, having been split off from the main personality.  Harry being Starborn might have also had something to do with it.

This leads me to another question:  Bob does not have free will, But when Evil Bob made his appearance in Harry's lab, he acted like he did.  Can a being without free will murder its master?

Assuming Evil Bob was actually going to kill Harry, that means that either Evil Bob had free will, or Evil Bob still saw Kemmler as his master.  This later suggests that Evil Bob knows Kemmler is still alive.

[Kindler]

I think that bob via butters is so similar to bob via harry is because butters knew of bob while he was with harry still.  Butters as the owner formed and impression of how bob was to be based on his previous interactions of bob via harry.  This is why I think that Bob has not changed much, other then the fun new Jewish Phrases.

Right, that's the crux of my question: how much of Bob's personality under Harry was based on interactions he had witnessed with Justin? And the justification I use for him witnessing those interactions is that Harry knew that the skull was valuable enough to take with him in the first place; as a 16-year old kid, he had no money, and little more than his pendant, a shiny new blasting rod (courtesy of lessons from Lea, judging from Ghost Story), the clothes on his back, and whatever cash he had stolen from the convenience store. Why on earth did he pull Bob "from the ashes," when did he do it, and why did he do it? If he knew the skull was important, I'd argue that it's because he saw Justin using it, and that formed some amount of his impression of Bob to imprint his personality when it changed ownership, similarly to how it worked with Butters.

It's entirely possible that Harry was searching for Elaine—I think Gryffin brought that up in an older thread some time ago, so I can't take credit (maybe Quantus? I can't remember what day it is half the time, so sorry if I'm misattributing the thought)—and thought Bob's skull was Elaine's, which is why he picked it up. Then Bob took care of the rest.

Anyway, it's all been an ongoing question for me, mostly because it relates to potential characterization of Justin in a way that we haven't gotten in the series. The portion of Bob's personality that's from his time under Justin, if it's at all significant and there is any remaining at all, tells us something about Justin. He might've been more like Harry than the series indicates, at least when he was younger. Maybe he was closer to Harry's personality when he pulled Bob out of Kemmler's clutches as a young man, and something changed over the following half century. Or maybe he was closer to Harry than we thought the entire time, and wasn't as straight up corrupt as we assume.

Or maybe it's all nonsense and I'm reading too much into mechanics that weren't fully fleshed out from the start.

[Kindler]

This leads me to another question:  Bob does not have free will, But when Evil Bob made his appearance in Harry's lab, he acted like he did.  Can a being without free will murder its master?

Assuming Evil Bob was actually going to kill Harry, that means that either Evil Bob had free will, or Evil Bob still saw Kemmler as his master.  This later suggests that Evil Bob knows Kemmler is still alive.

Evil Bob could've killed Harry by simply following Harry's directions. He was making Harry understand—in a way that would prove to be lethal. Aside from which, he didn't have free will; he was bound to Harry's previous command, which wasn't contradicted ("This conversation is over.") Neither Bob nor Evil Bob has free will; they're bound to whoever physically possesses his receptacle. It's why Harry never really took him out on fights. If someone nabs the skull, they're Bob's new master. When he's on the ground, his ownership is more fluid; Harry can claim ownership from Cowl because Bob wants Harry back, and the rules of his service allowed the transfer.

EDIT: The above is my understanding of things, at least; I'm happy to be proven wrong, as always. :-D

[Snark Knight]

Assuming Evil Bob was actually going to kill Harry, that means that either Evil Bob had free will, or Evil Bob still saw Kemmler as his master.  This later suggests that Evil Bob knows Kemmler is still alive.

He could believe Kemmler is still alive and be mistaken. He also blamed Harry for his personality split ("whatever you have done to my thoughts") instead of orange Bob.

[exartiem]

Harry Named Bob, thus gave Bob his own identity.  Kind of like he did with Lash.  She was a split-off meant to deal with Harry and he Named her and gave her an ID of her own.

[Griffyn612]

Harry Named Bob, thus gave Bob his own identity.  Kind of like he did with Lash.  She was a split-off meant to deal with Harry and he Named her and gave her an ID of her own.

Harry might have given Bob a name and a new identity, but he was the same entity that he was with DuMorne.  As near as we can tell, he was one entity for a thousand years or two (can't remember which) until someone partitioned him. 

At that point he was something new, presumably from the time DuMorne first possessed him.  Harry letting Bob split Evil Bob off was just the last part in the creation of a new entity.  If anything, the person that partitioned him created Evil Bob.

Evil Bob is to Bonnie as Partitioned Bob is to Lash as Kemmler-Bob is to Lasciel.

[Quantus]

Harry might have given Bob a name and a new identity, but he was the same entity that he was with DuMorne.  As near as we can tell, he was one entity for a thousand years or two (can't remember which) until someone partitioned him. 

At that point he was something new, presumably from the time DuMorne first possessed him.  Harry letting Bob split Evil Bob off was just the last part in the creation of a new entity.  If anything, the person that partitioned him created Evil Bob.

Evil Bob is to Bonnie as Partitioned Bob is to Lash as Kemmler-Bob is to Lasciel.

Agreed, though Im not  100% sure it was Dumorne that did the initial partitioning (Im like 95% sure though)

[exartiem]

I think Bob did the partitioning himself.  He was given two orders: teach Harry and never tell anyone he is Kemmler.  To give Harry access to his knowledge but keep that separate, Bob partitioned himself.  Evil Bob was the primary and Bob the puppet.  Then Harry gave him a Name, then killed Justin.  Bob then became the primary and Evil Bob got locked away.

[Quantus]

I think Bob did the partitioning himself.  He was given two orders: teach Harry and never tell anyone he is Kemmler.  To give Harry access to his knowledge but keep that separate, Bob partitioned himself.  Evil Bob was the primary and Bob the puppet.  Then Harry gave him a Name, then killed Justin.  Bob then became the primary and Evil Bob got locked away.

Not sure that would make sense from Dumorne (or a Kemmler-justin)'s POV.  The initial (pre-Harry's ownership) event wasnt just a partition; Bob said he had been compelled to cut off as much as he could, and burry the rest.  What we saw in DB was only the "what was left" part, there had already been a significant chunk removed, which is something neither Kemmler or Justin would have any reason or desire to do.  The only reason to destroy that Knowledge/personality would be if they viewed it as dangerous, either to them personally or if it got into the wrong hands. 

Fwiw, we dont really know for sure if the Evil-bob we met in GS was just the additional bits that Harry inadvertently ordered Bob to remove, or if those pieces somehow found and merged with the initial Chuck that Bob said he carved off prior to Harry becoming his owner. 

[exartiem]

Harry didn't order Bob to amputate Evil Bob.  He ordered Bob to never let that part out again for anyone or anything.  Bob chose to do the amputation as the best way to ensure compliance.  Harry doesn't fully understand how Bob works.

Same with Kemmler/Justin.  He ordered the spirit to never allow the secret out.  The spirit chose partitioning itself as the best way to comply.

[Griffyn612]

“Because knowledge is what I am. Losing my knowledge of
what I knew of Kemmler took away a…a big piece of my
existence. Like if someone had cut off your arm. What’s left of
what I know of Kemmler is close to the missing pieces.”

This can be interpreted two ways.  The first is Quantus' way, which is that a chunk of Kob's knowledge was cut away, and what Evob knows is what's left of that.

The second way is my way, which is that the knowledge Bob possesses about Kemmler (asshat, WW1, death) is close to the "missing arm", which wasn't actually cut away, but is suppressed as Kob/Evob.

Key
Pob: Proto Bob
Eob: Etienne's Bob
Kob: Kemmler's Bob
Dob: DuMorne's Bob
Bob: Harry's Bob
Wob: Waldo's Bob
Evob: Evil Bob

[jonas]

Harry impacted Bob more than butters because
A, he gave him a name and
B, nobody had any knowledge of Bob's continued existence nor has anyone besides Harry (and cowl...) seems to know this, however more and more people know him as Bob... He's growing an identity of his own even if he stays a reflection of his holder... Bob's basically a mini immortal sans the host we have come to see in most all of them.

[Griffyn612]

Harry impacted Bob more than butters because
A, he gave him a name and
B, nobody had any knowledge of Bob's continued existence nor has anyone besides Harry (and cowl...) seems to know this, however more and more people know him as Bob... He's growing an identity of his own even if he stays a reflection of his holder... Bob's basically a mini immortal sans the host we have come to see in most all of them.

We have a WoJ that the reason Butter's Bob is so much like Harry's Bob is because Butters met Bob during that time and established a relationship with that personality.  It might not have anything to do with having a name.  (Or maybe it's a part of the latter). But I wouldn't attribute it automatically to a naming power of Harry's.