It's a much-requested feature, but to this day we still can't change our PSN names, so if you picked a rubbish one back when you first signed up, you're stuck with it (unless of course you start from scratch and ditch all of your hard-earned trophies).
There was some speculation recently as to whether the feature might be about to be released, but it now sounds like that's not the case, after PlayStation boss Shuhei Yoshida responded to one question on the subject (over on Twitter) by saying something along the lines of:
"I wish I knew when. We're aware that lots of people are asking for the feature. Our engineers have been looking for a solution. As soon as we know, we'll let you know. But as of today, we don't even know if we can do it. Hopefully we will be able to provide the feature in the future."
So maybe one day, but it certainly doesn't sound like they're ready to implement the feature anytime soon.