I have been told that the fact that the connect column renames itself if you change the board that it is connected to is expected behavior. This is very frustrating as we have the same column in multiple boards (but linked to different boards) that we want to be called the same thing.
So the suggestion is to change the behavior so that if you are creating a connect column it names itself after the board it connects to but if you alter the connection it keeps the name it had.