Variable: make-backup-file-name-function

A function to use instead of the default `make-backup-file-name'.
A value of nil gives the default `make-backup-file-name' behavior.

This could be buffer-local to do something special for specific
files. If you define it, you may need to change `backup-file-name-p'
and `file-name-sans-versions' too.

See also `backup-directory-alist'.