Leia out of respect for family titles decide to retain their names, similarly to how some women decide to retain their family surname anyway when marrying. Anyway I believed particularly as she is reffered to as in the cast list as Padme, that Amidala was a dignitary name that was given to her when she was voted in as the Queen
Actually froom that I have a question, how does a democratically arranged monarchy work. I mean surely this misses the entire point or else within a few centuries everyone on the planet will be royal. Queen Amidala has children obviously they are royal even if she steps down and becomes the Queen Mother whilst a new royal family on the planet is voted in. Marriage on the Planet would eventually lead to a host of royalty...
Well I suppose it depends on your point of view, now Plato had suggested that every one no matter your station should be a part of politics, However he said that you will remain perpetually within a chosen station. This looks more Socrates style suggesting that from Plato's argument that every man may have his hour...
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You know if you are going to be that picky about it thn you will have to trace back her lineage to the biginning of time and put the maiden names of all the wives in there. And when have you ever heard of anyone who is adopted keeping their real father's surname? When she is adopted she takes the names of her new parents. No questions asked. So her name is Leia Organna Solo.
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That is the point, that may have been her name, but given that she seemed having lost her office just returned to the name of Padme Naberre, then it is possible that Amidala is the term for the Democratic position even if also applying a paradoxical monarchical station as well. As to changing her name, one interesting point is that whilst in theory she could become a skywalker, well Luke and Leia both know they had parents but at no point is it even vaguely insinuated that they were married.