Drake was born Mathéo Dussault around 300 years ago. These days he goes by the given name Drake - and rarely offers a surname unless it's a very formal occasion. He writes these days to pay the bills and has moved in with Ezio. He's not friends with Vlad, but he also does his best not to be antagonistic with the Count.
He and Ezio had quite the history, but somehow they've fallen well into place as friends.