Make two doors. And also make two cells. That's the only way to change the name of a cell, by making an identical one with a different name. Take the original cell, select everything and copy it, and paste it into a new cell. Then, you have to make a second door, and stick it right on top of the first one, one door pointing to one cell, and the other pointing to the identical cell with the different name. You need to put a script on both doors, so that when one is active, the other is disabled. Then, when you want to "change ownership" of the house, trigger the other door to enable, and the first one to disable.
It's most reliable to trigger the change with a Journal entry. The scripting is simple.
This is for the first door you find in the game, before you change the name of the place:
Begin YourFirstDoorScriptIf ( GetJournalIndex "YourJournalEntryName" >= ## ) ;number of the journal entry that says you've changed ownership of the place or whatever. If ( GetDisabled == 0 ) ;makes sure it only does it once Disable EndifEndifEnd
This makes sure the other door disappears, and replaces the first one after you change the name of the place:
Begin YourSecondDoorScriptIf ( GetJournalIndex "YourJournalEntryName < ## ) ;same numbered entry as the first door If ( GetDiabled == 0 ) Disable EndifElse ;the journal entry is that number or higher so the place has changed If ( GetDisabled == 1 ) Enable EndifEndifEnd