How can I change the URL of a networked Time Machine backup
Just add the destination as a new disk in the Time Machine System Preferences GUI. It is smart enough to figure it out since there are identity tokens stored on the Mac and on the Time Machine destination.

It might warn you that the "identity" of the new location has changes and you have to approve before continuing to back up.

Time Machine can handle many destinations from one Mac and just picks up from where it left off for the last backup at that specific destination.

Worst case, you have to manually inherit the backup after associating with the new share. See the tmutil manual page for details if needed.