@Ruth ******
I think that in order to change branches they have to open a new account at the new branch. It’s a lot of work but offered to just change my mailing address. I still have the original Bangkok account and branch.
If you were to open a new account at Kasikorn or another bank I imagine they might want to examine your visa but not for a mailing address change.
If I was still applying for one year extensions of stay I wonder if I would have had to go to the Bangkok branch for the bank letter and yearlong statement. I never got a chance to find out since I had already switched to a 10 year pensioner LTR so I have no need to visit an Immigration office.