When did Star Wars become known as Episode IV - A New Hope?
When Star Wars was originally released in 1977 it was but a single movie. A single movie that smashed attendance records all around the world and everyone who saw that movie in that theatrical run saw that now famous title crawl without reference to 'A New Hope'.
Star Wars was simply called Star Wars.
Spring forward to the making of The Empire Strikes Back. During production George Lucas was sufficiently of a mind that he had lots of Star Wars stories to tell - some of them were set before Star Wars so he came up with the idea that The Empire Strikes Back was actually Episode 5. This meant he would be able to make prequel films if he wanted.
So Empire was released in 1980 to even bigger success than the original film with a crawl that referenced the story as being Episode 5. This lead to a second theatrical release of the original movies in 1981 and it was at this point that George Lucas added 'A New Hope' to the film's crawl.
It was this version of the film that was used for home video release - thus ensuring many fans first experience with Star Wars featured the title A New Hope.
So you can be forgiven for thinking ANH was always called that but it's pretty clear it wasn't officially named as such until at least 3 whole years after the film's original release.
If you're wondering where George Lucas got the idea for the crawl from, it was the original serial versions of Flash Gordon.