I never change their name unless I can tell the bird doesn't really recognize this sound as its name or it's completely wrong for it, in which case, I try to find a suitable name that sounds very similar to the one they had. Javi Caique's name was Cheeks but he would not even look at you if you called him by this name and he kept on referring himself as Javi -which is his previous owner's name- so he became Javi. And he answers to it. Same thing with Keku Quaker, her name was Gryphon but she kept on calling herself Keku so that's the name she now has. Then you have birds that were named with the wrong gender: Naida Zon used to be Nathan, Elly Gray used to be Elliot, etc. Or birds that were renamed just because the new owner liked a name better: Zeus Zon had been renamed Oscar by his second owner but I went back to his original name of Zeus and he knows it as his name. Or birds that were given mean names... I had a mini-macaw pair that came to me with the names Hell and Chaos - now what kind of an idiot would do such a mean thing?! So they became Hellen and Cato. Davy Redbelly must have been either a bird that was stolen or found by somebody and then sold to me. They claimed his name was Baby but that was only because he says: "Hey, baby" and 'Hi, baby". Most likely he had another name but I decided to call him Davy because it sounds a lot like baby. Then there is Sweetpea Senegal which came to me with the name Sabu [a name he did not recognize or even repeat despite the fact that he had lived 11 years with it and is the most intelligent bird I have] while he would ask: "What's your name?" and reply himself: "Sweetpea!"
The thing is that parrots understand and use the concept of proper names in the wild. The parents name the babies in the nest and these babies continue to refer to themselves by this name [or a very similar sound, kind of like a nickname, one would say] all their lives so, although they are intelligent enough to learn to recognize a new name, it's kind of disrespectful, no? It's like going to somebody you just met and saying: "I don't like your name so I am going to call you something different". Not very respectful, is it?
In conclusion, I would say that, if the name is OK -even if you don't like it a whole lot- I would keep it because, as Navre said, it's hard enough for them to go to a new home with strange humans and keeping the name is comforting to them. But, if the name is completely wrong or the bird calls itself something else [my cockatoo calls himself Hi, Linus
], change it to the name the bird calls itself. or a name that is very similar to the one they had before and recognize as its own.