Now I wasn’t alive at this time, but from talking to people who were, it’s my understanding that even though the “A New Hope” title was on the movie since 1981, no one actually called it that until the late 90s at THE VERY EARLIEST. Seems like it was more when maybe the 2000 VHS came out.
The sides of 1995 VHS packaging for the movie we now know as ANH has a logo that says “Star Wars” and says “A New Hope” in small letters while ESB and ROTJ say “Star Wars” in small letters and have logos that say “The Empire Strikes Back” and “Return of the Jedi”. Otherwise, ANH was marketed as just “Star Wars” until the 2000 VHS release.