I'm not a big fan of
Bob as a full name; I don't like many B names, and I don't like the abrupt sound. I'm also not keen on nicknames as full names, and
Bob has a very informal feel to it that makes it seem rather insubstantial as a full name.
At the same time, though,
Bob is classic. It's easily recognizable. Everyone can spell and pronounce it. It's not cutesy or childish. I'd rather see a baby
Bob than another baby
Brayden.