The Emperor remembering the life of Balduran doesn't mean the Emperor identifies as Balduran. It's the player that assumes they're the same.
Of note, the Illithiad was a source book that TSR put out years ago. It was entirely about mind flayers, and it discussed the tendency for some mind flayers to have lingering connections to who their host used to be. Things like tapping fingers on a table thoughtlessly. When this was discovered in a mind flayer, it often led to the community enacting a death sentence. Thus, some mind flayers, when they realized this was happening to them, would attempt to hide it.
It's not an enormous jump to say that some mind flayers remember more and more of their host lives, and it's reasonable to assume that those memories might impact the illithid's behavior and personality.
Mind flayers have always been able to break away from the elder brain. Alhoons are notorious examples.
