BETA version -- 5.0.1002.182

[LuckyJim]

Don't use ENTER.
Just click anywhere on the empty area of the web page(to make the input field lose focus).

I should have mentioned I already tried that.
Clicking on an empty space doesn't save the new Profile name. Upon closing the Settings tab it reverts to the default "Person 1".
Interestingly enough, changes made to the Theme Color and Avatar are saved successfully.

EDIT to add: I'm using v5.0.1002.276 x64 Portable, Windows 11 22H2

EDIT 2: I just tried to rename my profile from the default "Person 1" to "Person 2".
And, lo and behold, the changes were saved. I tried to rename it again to my favorite username and the changes were saved again.
I'm putting this here in case someone encounters the same problem.