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Same here, PC (Steam version of the game).
I'm experiencing this issue as well. My semi-workaround is to enter the lot from build mode, change the lot name (even if you've already set it, delete it and retype). Save your game, THEN go back to world map view. From there, click on the lot, and change the individual unit names. In this view, you can still see the original name at the top, but at least it's correct in map view.
This is after changing the name in Build Mode, and saving before going back to Manage World/Map Screen.
From the map view, click on the property, click the i in the bottom left, and edit each lot name.
I can only get this to work on Rentals with multiple units. It's not working on single unit rentals, but I am working on a mod/fix in the meantime.