As hinted earlier, there are significant caveats. Officially, only games released for the first time after April 1st, 2018 have been designed to support ID changes, and there's still one unspecified title that has problems. While a "large majority" of popular PS4 games should work, Sony can't guarantee that a name change won't cause hiccups. There's a compatibility list that shows the potential problems you might face, including a few titles (such as Just Dance 2017 and LittleBigPlanet 3) with "critical issues" that break the experience.
PS3 and PS Vita games don't support the feature.
It's arguably an overdue change when Xbox owners have long had the option of changing their gamertags, and the technical limitations could leave many people sticking with their names for a long time. Still, Sony had to start somewhere if it was going to make the feature available in the first place. And let's face it -- if you've been stuck with an embarrassing ID for years, you'll probably be willing to make a few compromises to choose something more appropriate.