I personally think that your game of TDFRPG is your take on the Dresdenverse. If you want more hierarchy, then do it.
As for evidence of such from the books, there isn't much. I attribute this to 2 factors:
1) There isn't much in the White Council. Apprentice, Initiate, Senior Council, Merlin. Very simple. There are stole designations for master enchanters, alchemists, etc but no actual titles like "Enchanter Barnaby" or "Summoner Siegfried" or whatever because that would complicate things.
2) [More important] Harry is an unreliable narrator. From minute one of the Council meeting in SK, Harry has admitted that he is both amazed at the White Council and doesn't know what the hell is going on half the time. During Council meetings, Harry translates the Latin, but we all know how bad it is. They might actually use terms like Master, Thaumaturgist, etc in common parlance during meetings and to refer to one another but Harry doesn't let us know that because in Latin they are all synonyms for "Wizard" to him. He also finds every reason in the world to not learn more about the Council because it doesn't affect him.
That's my answer.