Deleted Settlement still giving its name to remaining 'settlement'

Had city status however after they moved, it still shows the initial settlement name even after all the beacons have been removed.

Have you tried renaming it again? Normally when 2 settlements merge and then split again, they will both have the same name until one of them is renamed.

I think this is normal as the settlement name has essentially been overwritten when the settlements were merged and the game has no record of the previous name.