You have to get BATFE permission to move the frame ser# before doing it last I knew. There is(was?) a form and process for doing so.

Bowen used to do it and go through the proper steps, but when the BATFE started to reject the requests he stopped adv & doing the work.

Doing it for a purely custom or cosmetic reasons will most likely get a rejection.
I got one rejected when I wanted to move a ser# to less prominant location on an engraving job for a customer.

That's why Bowen won't do the custom frame lightening cuts on the sides of the Ruger SAA's as he does on the Colt SAA frames.
The Ruger ser# is there on the right hand side in the way.

That's the process anyway,,but lots of people don't bother with it!

The original manufacturer can change the number location for a factory option I believe w/o difficulty still, but even that may be in doubt.
I don't really know where they stand on that now.