Unfortunately it becomes Dave in the US 
It often becomes Davey here in the UK, though.
It probably wouldn't matter what we named our kids, they would have some weird nickname in a few years time anyway. Everyone in this village does, even me! DH is Munchie, and I am Munchie's Lass or Mrs. Munch, and then DH has friends called Armit, Stoney, Hilda (a man!), G, Wilkie, Hoggy, Lockie, and there's even a lady here that the folks call Bacardi Breezer!

And whatever the nickname is, it just sticks. Besides his mother (and my parents and friends) I am the only one who calls DH by his given name (which is Adrian, the best name ever, IMO!) Even his superiors at work and his former teachers call him Munchie.