I'm going to assume you landed on this years old page cause you got the same message, or your error has similar keywords. Still, without an exact image, we can't fully help you, but rather can only speculate.
To add-on/simplify what Kaphotic's said. Current Handler in certain situations can be Original Trainer (OT); it doesn't always have to be Latest Handling Trainer (HT). For example, if you traded a mon away to someone else, but traded it back to the OT, the Current Handler would be OT.
Based on what you've said, it appears you're treating Handling Trainer and Current Handler to be the same. They are not the same. Hence why the whole renaming idea wouldn't work
To reiterate, just in case you missed what Kaphotics said, Current Handler is determined by the green box selecting the entire area of HT or OT.
Additionally, it appears the response you quoted was age-old, so lemme give a run down on what to do now.
Instead of clearing the HT's name, all you gotta do is click on the area to shift the green box.
(If your issue is at all similar to that user's issue)
Using images (in spoiler):
I like giving people other perspectives to look at an error message, cause sometimes tackling issues from a different perspective helps to offer clarity.
However, because I don't know your exact error, I can't help with that
Even though we didn't have your exact image, I hope the explanation from me and Kurt resolved your issue.
Have a great one.