Well, we know that 10 years later, N/newL would most likely be alive. At least he was alive 1 year after the event, when we see him talking about one of the people who had the Death Note but said he wouldn't take up the case because it wasn't worth it, and eventually the guy ended up dying. The point is, when 'L', the currently 10 year old girl was born, N was still alive and had picked up the title L (since the first L's death was never officially announced, I believe). The possible successors from the orphanage were all given different letters so naming one L is just plain weird. I don't think that their names actually change at one point and having the name 'L' probably doesn't automatically make you the successor, as seen in N and M's cases. If it did, that would mean they would have decided she would become the successor the day she was brought to the orphanage or perhaps the day she was born, since she apparently already has a reputation for being a great detective and was probably in the orphanage for quite some time. It's absurd to have 2 Ls at the same time and have one of them be the successor of the other while the letter doesn't really carry any meaning. 
[hider=What making yourself the successor sounds like to me]You're practically saying, even if unintentionally, you're the best detective without RPing it.[/hider]

EDIT: Actually [url=http://deathnote.wikia.com/wiki/Near]here[/url], we see just when he was last seen, which I'm just adding to support my point (don't want to call it an argument -. -.)

[hider=Also, fun fact]In an extra chapter, it was revealed that if you erase a name from the Death Note, that person will be revived :3[/hider]