Looks like you'll be able to ditch any horribly embarrassing Minecraft usernames in the near future, as developer Kristoffer Jelbring's been teasing the "change" option via his Twitter account.
— Kristoffer Jelbring (@KrisJelbring) January 5, 2015
A quick check of the username support page shows there's no official date given for the option being launched but Jelbring responded to a question about the rollout saying, "More info will come soon. Hopefully later this week."
The ability to change usernames has been a work in progress for a while meaning the team has already hammered out some of the specifics with regard to how the process will work. It's typical common sense stuff, really. For example, the service will be free of charge but limited to a certain number of changes in a given period of time, and you can't change your username to one someone has already taken.
You'll also only be able to use the service if you're on a Mojang account rather than one of the older Minecraft accounts. How you work that out is: if you use your email to login you have a Mojang account and if you use your username it's a Minecraft account. Obviously the latter system would enter new worlds of pain if you could change the username hence you have to have upgraded to the Mojang system.
Servers already identify players via a unique identifying number (a UUID) which is how they deal with player data. Generally that transition has been taken care of by Mojang but updates to custom mods and plugins are necessary to accommodate the changes.
All of this reminds me that I don't actually know my username and am involved in a gaming account stalemate. A friend bought me the original game back in 2009 before the current login setup was implemented and, after a few years of absence, I can't remember any of the details and don't have any kind of receipt so can't access the full game anymore. It's not an insurmountable problem exactly, but it'll take a bit of effort and negotiation to fix. It also means I'm in a slightly peculiar usernameless Minecraft hinterland right now.
But yes. If you fancy not being, like, DanielMerriweatherFan69 or something equally of 2009 then the end is in sight.
N.B. Daniel Merriweather joke was not appreciated by RPS hivemind. I might be on my own with that one.