Vincent was a Corleone because he was Santino's boy, but being that he was an illegitmate son, he was never "legitimately" recognized as being a part of the Corleone family. He went around as Vincent Mancini, which probably was his mother's doing at his birth.

However when we see Michael tell him "Now you can call yourself Corleone," it is more symbolic than anything else. Of course it meant, to Vincent, that Michael was now finally recognizing him as his "legitimate" nephew, as part of the Corleone family. But it's meaning was more of one that symbolized Michael's passing of the torch, his passing his "Corleone" power onto Vincent.


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