In real life, a baby, particularly a first baby, probably doesn't need to constantly be addressed by name. It's not like you'd be saying, for example, "hey Bella, come over here"--you don't call her by name for her own benefit at first, and there's no other baby around that she needs distinguishing from unless she's at a daycare or the like. Parents would be more likely to say "don't wake up the baby" than "don't wake up Bella." and they may drag the "can't decide on a name" thing out for several episodes.