The character Red did not originate from fanon, and the information on this page may not be entirely accurate to their canon. You may read more about this subject in the context of their canon on the following wiki(s):
Red (Japanese: レッドRed) is a Pokémon Trainer that first appeared in Pokémon Red and Blue. Red serves as the player's avatar in multiple Pokémon titles, namely Pokémon Red, Green, Blue, Yellow, FireRed, and LeafGreen. Because he is not shown to speak outside of dialogue trees, Red is depicted as a silent protagonist in his appearances in later games.
Red has canonically defeated the Kanto Elite Four and become the Champion, though eventually leaves the position to continue his journey and battles the player in Pokémon Gold, Silver, Crystal, HeartGold, and SoulSilver.
In the main games where he appears as a playable character, the player can choose a name for Red. While the player has the option to enter an arbitrary name (such as their own) for the character, a number of other predetermined choices are also available, including Jack and Ash.
While the Pokémon Trainer from previous Super Smash Bros. titles does not return, Red does make an appearance in Jake's Super Smash Bros. as a character that can be summoned using the Assist Trophy item. When he is called upon, Red will throw a Master Ball onto the stage and call forth a random Mythical Pokémon, Legendary Pokémon, or Ultra Beast. The Pokémon that can be summoned are the same as those that can be called upon by using the Poké Ball item.
Red can be found on the summit of Mt. Silver in the Virtual Console of Pokémon Gold, Silver, and Crystal, released for the Nintendo 3DS. He is the secret final boss of the game. His team is the same with the same levels as the original edition of GSC, but the movesets are different and improved.
While Red has continued to make appearances as a character throughout the series, he has had different canonical names between games in the past.
While not official, Red's default name in Pokémon Blue Version was "Blue". Similarly, in Pokémon Yellow Version and the Japan-exclusive Pokémon Green Version Red's default names were Yellow and Green, respectively.
Prior to the release of Pokémon Gold and Silver Versions Red was officially referred to as "Satoshi", which is the Japanese name of Ash Ketchum, his counterpart in the Pokémon anime series. When Pokémon Red and Blue Versions was released in the west, one of Red's default names was "Ash", a reference to this.