We've never been told his cat's name. Fanfic writers have come up with all sorts of ideas, ranging from Einstein to Cat. (Memorably, I have seen him not name the cat Schroedinger as it's too obvious for a physicist. Heh!)

I fear that the photo was a prop flub -- he definitely only left one cat with his neighbor. But I spin it that the photo is of an older, much beloved pet that died/was lost in a breakup/was left in a move from home or college.