Kitty's main Superhero identity is still Shadowcat despite them leaning hard into the "Captain Kate" stuff and pretending like it never existed, so by the power of theme naming Kitty will probably be back at some point and still be the name they use for her in outside media.
I always did find it kind of weird that she was using Kitty well into her 20's and out-of-nowhere decides now is the time go by "Kate" and have everyone call her that. Like if she really meant that she should've done it during or after college.
I think most likely she just uses both interchangeably.