I have always heard R’ Velvel referred to as “The Brisker Rov” and R’ Y. B. Soleveitchik as “The Rav”.
R’ Velvel is referred to as “The Brisker Rov” but generally not by his talmidim, they would refer to him as “The Rov” (this wasn’t a unique title for R’ Velvel). To add to the confusion R’ Yehoshua Leib Diskin was also referred to as “The Brisker Rav”.