Everybody in the world knows who The Rebbe is, when talking about other rebbes they say Gerrer rebbe, satmar rebbe etc., but everyone knows who The Rebbe is.
FWIW, I do not refer to the Lubavitcher Rebbe as “The Rebbe.” I refer to him as “The Lubavitcher Rebbe” or (rarely) “Rabbi Schneerson.”
The Wolf