There’s been some work done on the phenomenon by neurologists. Apparently, the different neural networks that light up when bilingual or multilingual people switch languages can quite literally evoke different personalities.
When I’m reading in French, listening to French music, or having conversations in French, I start forming my thoughts in French instead of in English. When that happens, I start to feel like a different person. Like the me of the internal dialogue in my head switches out to somebody else, somebody I recognize but who isn’t the same “me” as the english-speaking “me.”