In almost all circumstances, I call it Star Wars, mostly because that was the name of the movie the first several times I saw it, and it was the name of the movie during the period when it took the world by storm and saturation-bombed commercial media, and it was the name of the movie when it won all its accolades. For at least four very intense Star Wars-centric years, that’s the only name the entire planet used for it, and that’s a lot of people you need to convince to change what they’ve been doing for years.
I never saw the film with its altered name in the theatres, and only saw it that way on home video. Because of that, I never stopped calling it Star Wars. Similarly, I never started called Raiders of the Lost Ark “Indiana Jones and the …” just because it said that on the box. Besides, for the first fifteen years or so of home video, “Star Wars” was always still printed in much bigger type than “A New Hope”, unlike “Empire” and “Jedi”, which were printed much bigger than “Star Wars”. If you look at the boxes from the time, you’ll see it. The world still considered it Star Wars, and the marketing folks weren’t about to lose a sale by confusing people. I really never even head of anyone calling it “A New Hope” until maybe 1995. As far as I know, “Star Wars” was the only name anyone called the film until around then.
Then, around the Special Editions, people started pushing the “A New Hope” name hard, and also episode numbers. The focus on episode numbers always bugged me, because through much of my childhood, I’d considered Star Wars to be Episode I, since Empire came out as Episode V, and Star Wars had no episode number, I just naturally assumed we skipped three episodes between Star Wars and Empire.
I have no problem calling the Special Edition version “A New Hope”. As far as I’m concerned, the Special Editions are completely different films and I’m happy to be able to use a different name for one of them to avoid tainting the original name.
I should add that saying Star Wars is much easier than saying “Star Wars: The original one from '77”, and gets the point across just as well.