This is the thing about multiclient protocols. You don't look for SMTP in the app store either :) The whole point is having multiple clients so they can't all have the same name.
Having said that, the 'default' app constantly changing their name (Vector -> Riot -> Element) is super annoying. I thought Riot was a stupid name (living in a city that regularly sees riots), but don't really get what was wrong with Vector in the first place :P
Also about Matrix, the confusion when the client app doesn't have the same name as the protocol is so unfriendly for the non tech-savy users.