It actually does have something to do with Greninja specifically. It's not JUST Ash + Greninja or Ash + Pikachu, or else other trainers with very strong bonds with their Pokémon would be able to achieve fusion as well. As see in one of the Ninja Village episodes, this Greninja fusion has happened before, a long long time ago. "Ash-Greninja" is just the name Bonnie gave the transformation because Greninja happened to look like Ash. (From a design standpoint it WAS designed to look like Ash to make it marketable, but according to lore it is just a coincidence.)
I don't know if this is satisfying enough for an answer so I made it a comment.