He didn't say he talks to himself at brunch. It was only implied that he talks to Socrates.
He just said basically that "Socrates...says so [the beginning of wisdom] everytime we have brunch." Given that many of these entities, or mantles are/and have multiple personas I wouldn't put too much weight on the we as delineating Hades from another person sitting opposite aside him at lunch." I can see Hades/Socrates having lunch with another, (he does share a drink with Harry), and he often gets asked questions, just like Harry asks him questions. He often tells people "...the beginning of wisdom" just like he told Harry. This is all consistent with what he said. He just interjects the name Socrates for his name, instead of Hades.
“Wow,” I said. “Socrates is, uh, down here?”
Hades arched an eyebrow. He lifted his free hand, palm up.
Read with either Socrates or Plato as Hades/Pluto.
Hint: The one and only, right here. Vs. This is the underworld.
“Right,” I said. “Sorry. Um. Do you mind if I ask . . . ?”
“His fate, in the Underworld?” Hades said.
I nodded.
Hades’ mouth ticked up at one corner. “People question him.”
Read as Socrates or Plato as Hades/Pluto.
Hint: You dupe, I just told you 'people question him' immediately after you asked me his fate AND my mouth ticked up at one corner. Sometimes, you know, 2+2=4
Jim: You dupes put it together.
That all said, sure, Hades may not be either Socrates or Plato, but with all these mantles passing this way and that. It's a possibility. And one that is already built-in should Jim want to use it.