I haven't read anything about his background, but I tend to suspect he may be of Latvian descent. (In Latvian, a "putin" is--yes--a bird.)
Plus, he just plain looks Latvian. My mother's family came from that country, so I've seen a lot of Latvian men. They're a...uh...well...distinctive-looking lot. My maternal grandfather, actually, was a dead-ringer for Putin. I'll have to read up on the guy some more and see if I'm right.