Gamertag regret is very much a thing, especially as we get older and realize that what we thought was cool ten years ago is embarrassing now. PlayStation gamers have been unable to change their tags outside of making a new account altogether, but that could be changing according to Shawn Layden. Speaking to KindaFunny's Greg Miller (via Gamespot), Layden said: "I hope we'll see events occur that you won't have to ask me [about Gamertag changes] next PSX."
Layden later told Gamespot after the PSX Keynote that the feature is being worked on by "the elves at the North Pole" but that the work behind it all is "more complex than you think."
Xbox One gamers can change their Gamertags, though granted it's only free one time. Steam currently sits as the pinnacle standard for user-friendly Gamertag changing, as their system involves having two names. You have a Community ID that is visible to everyone, and a Steam Account name that is seen only by you that cannot be changed. Community ID's are not tied to anything related to account identification on Steam's end and can be changed at any time. And really, the only reason anyone ever wants to change their Gamertag is that it looks stupid to everyone else, so Steam far and away has the best system in place since it works well for both player and provider.
Details on when PlayStation plans on rolling out this new are unknown, but it's certainly an issue worth tracking.