Requiring licencing would be taking another liberty away from the people and giving it to the government. The solution to all or problems is not, "lets pass a law against it." Sometimes other solutions work better, and some mistakes it's better to just let people make. Yeah, it's a tough name for a kid to have, but lots of kids get made fun of for their names, and he can change it when he gets older, if he so chooses.
Similarly, the government also has no buisiness decided who can and can't have children. In fact, what needs to be done is the government making sure that it doesn't interfere with the normal consequences of unwise activities that lead to pregnancy. I life near a major city, for example, and it's a fairly normal practive for women of a lower economic means to purposely have more children so the government will give them more money in child support. The mothers are thus unfit, but the natural consequences of having children in this fashion have been supplanted by government created benefits, encouraging this behavior.
Now, as addressing population growth in general, the economically sounder countries have for years been experiencing massive population shrinkage, without any need for government control. Only countries with a large amount of immigration, like the US or the UK, are still experiencing much of a population growth, if any. This tells us that economic growth is the best solution to this problem too, and a solution which takes liberty from no one.
