Sure. If your table wants to call 5.5e "jojo Plays Baseball," go for it. On the individual and table levels of the game the names don't matter at all. However, when discussing in a larger group like an online forum which versions are an edition and which are not, names and designations do matter to that discussion.
AD&D has had 5 and only 5 editions. Basic and it's various lines were not editions of AD&D, so they do not count towards the edition numbers. Similarly, the expansions/half editions were not editions and do not count towards the edition numbers.