I would say.. Yeah, Once the names been changed legally, anda would need to write that new name in the deathnote in order to kill someone.
Though... your birth name could still be used against you. Since anda can't exactly change your borth certificates details, because anda can only be born once. So sejak changing your name, your just giving someone anouther name to be able to use to kill you. Since both names would be legal, in a way.
atau maybe not. I don't know lol. I'd need to know lebih about the laws regarding changing your name legally. Laws might even vary depending on your country. Plus theres the dethnotes rules to consider aswel, and no one but the maker of the Death note can make the buku rules LOL
It's what the person considers to be their name; the birth certificate has nothing to do with it. For example: If a very young girl was found on the jalan (and wasn't aware of her name) and was taken in sejak a family who called her "Sue", and yet on her birth certificate she was named "Lindsay", Sue would be the name written in the Death Note. So, returning to the original question, it is most likely their new name would be the one that would be written in the Death Note if they considered it to be THEM, if that makes any sense. If it was simply to avoid the power of the Death Note that they changed their name, though, then it's basically the same as an alias and won't work in the Death Note. It is not a matter of legal issues, but personal belief/attachment to the name.
Well, in a lawful state, when anda change your name, anda sign to relinquish all ownership and hold over the old name. anda may not legally use that name anymore. Your name anda chose to accept would be the name that would be written down. Shinigami eyes however, would probably still see old name as the real one. anda might get away with it... who knows? try it and see ;)