There's problems with doing it. Not all plugins will know who you are anymore. It's really not a well implemented system.
You might not be able to access any of your chests. And let me tell you. Staff are not going to manually break thousands of locks because of this poorly thought out idea from Mojang.
We still need to figure out what players need to take care of in-game before they change their name, so it's worth WAITING if it's something you want to do.