It’s very rare that a name change is granted other than buy resolting to some of the options stated on this thread (VIP, Donator).
 
I found one such case (there are probably others):
Before: izanagi -> https://web.archive.org/web/20160126223345/https://bitcointalk.org/index.php?action=profile;u=334527
Currently: izanagi narukami -> https://bitcointalk.org/index.php?action=profile;u=334527

He’s not on the list of VIPs nor Donators (https://bitcointalk.org/donate.html), so there was probably a reason that was strong enough for the change of name to occur. The name is not completely changed though, and I figure it maintains a high relationship to the original name.