Pokemon Red and Green were created. The main character was a boy from Pallet Town named Red.
Then the anime was created, with a trainer based off of Red named Ash. Ash was given a Pikachu
The anime was insanely popular. Cashing in on this popularity, Gamefreak released Pokemon Yellow. Pokemon Yellow is Pokemon RGB with added changes to make it more like the anime. Changes include: Red's design being altered so he looks like Ash Green's design being changed so he looks like Gary Red being given a Pikachu so he matches Ash Red able to get Charmander, Bulbasaur, and Squirtle from characters from the anime so he can have Ash's season 1 team.
In Pokemon Gold and Silver, they took the Red from Yellow, who was based off of Ash, and placed him as a secret character. This is for veterans to freak out with nostalgia over fighting themselves from Gen 1, and for anime fans to think they're fighting Ash. They gave him Ash's current anime team, complete with Pikachu being the strongest and favorite, with 2 changes. 1. Obviously they had to evolve Bulbasaur and Squirtle or else he'd be a complete pushover 2. Espeon was added in to represent a Gen 2 Pokemon
Now the remakes did the same, except took it even further. They decided to give him Ash's complete Orange Islands team, along with Pikachu's current anime moveset, so all the anime fans can glimmer with glee when they fight "Ash"
He's not based on the manga Red because the GSC arc happened AFTER Gold and Silver came out. the manga is based off of the game.
There. Red is not Ash, but IS heavily based off of him due to the insane popularity of the anime. Now stop getting angry everytime someone calls Red "Ash". Gamefreak intended for this to happen, and so what if they call him Ash, they can relate to him however they want.