OK ... Now I understand what is happening.
In TTDP ...
When creating a new scenario, TTDP does not yet know how many towns there will be.
The player may build a town near an existing industry and want to rename the industry to match the town name, or to give the industry a completely unrelated name.
The player then saves the scenario and then selects to play scenario.
The player is now in a game but the player has not named a company yet.
The oil rig name remains grey because it does not know who owns the name.
The player saves the game.
All the game's data is frozen and saved.
When the player loads the saved game into the editor, the saved data is protected and can't be changed.
Note that for the oil rig the displayed name is a station name. Click somewhere else on the oll rig and you will see an industry window which does not have any rename option.
So, here is the workaround ...
In the game, use the build station tool to create an adjacent station tile on land.
The oil rig name will change from grey to your company colour.
The oil rig station now belongs to your company.
You can now rename the station.
If you do not need the land part of the station, blow it up (BOOM!!).
The oil rig station will remain yours to rename as you please.
You can do all this without loading the game into the editor.