Well, Kisame got himself... fairly well-known during the third-war, and in particular has slaughtered whole Konoha squads in the past so! If Sakura were the kind to look into things, she might know him as either the Monster of Hidden Mist or the Tailless Bijuu. He's also probably one of the more quickly recognized of the Seven Swordsmen outside Kiri. The clan is probably known by name and for their large chakra-reserves, especially if one is interested in bloodlines.

Seeing that her personal blade was well-cared for would be one of the things that would convince him to do it so!