Besides the animal, it's most well known as the name of legendary football coach Bear Bryant. It was picked for several celebrities, though usually as a middle name—where I think it works a lot better. Red Hot Chili Peppers' frontman Anthony Kiedis and chef Jamie Oliver picked it as a middle name for their boys, while Alicia Silverstone also put it in the front, as Bear Blu.
There's no word on whether/if the baby has a middle name. Bear does sound nice with Winslet, though I'm still not convinced it makes a good name for a grown man.