I see nothing wrong with naming unborns who die. I have at least one set of friends who did just that. Birth certificates would be a bit much, since the child was dead before the miscarriage started and birth certificates refer (I'm pretty sure) to live births. Death certificates? Maybe, but what time would you give? It seems like an unnecessary complication.
Now, the other part of your comment is two-fold -
what do we do when the mother's life is in danger
I guess I think that's up to the mother. For instance, a tubal pregnancy. Neither the mother, nor the baby can live through a tubal. Now, if she wants to maintain the pregnancy and die, fine. Her choice. If she wants to end it - great, we get to keep at least one of two otherwise dead people around. There is no scenario to keep the baby alive. What's hard to understand about that? Other scenarios start to get a little gray. Someone who has a major health problem that can be exacerbated by the pregnancy. Well, if it becomes unclear as to whether or not she will survive, then she's got a hard decision to make. Me, I'd almost certainly fight to keep the baby. I bet my husband would argue against me, to assure my continued presence in our family. Hard decision... I think that should be within the realm of legal options.
what do we do when the baby is unwanted
I don't see abortion as a reasonable solution to personal discomfort, embarrassment, etc. This is specifically because we are talking, I believe, about putting another (innocent) person to death for the sake of another person's happiness and/or convenience. Would I like to see that stopped, even prosecuted? Absolutely... but only because I believe it is murder. (For instance, that I believe certain behaviors are against God's will, like unmarried sex of any sort, does not mean I am at all interested in policing them. They are not infringing on anyone's rights. Not my place to judge.) Because it is murder, I have a responsibility to protect the helpless - within legal and Godly bounds.