Shauna gave me a frokkie but its name is "Froabble" stupid names.............
Normally, yes. You can go to the name rater in Camphier Town and change a Pokemon's nickname.
However, this is Shauna's Froakie. Since you are not the original trainer, you cannot change its nickname. However, if you breed another Froakie, you can change its name.
Yes you must go to the namerater. But if its trainer ID and secret ID are not yours then the namerater will say it is perfect.
Yes you can change the name of a Pokémon in Pokémon X and Y providing that it is your Pokémon and it is on it's Original Game.
No you cannot change the name of the Pokémon that Shauna give you after you defeat the Champion in Pokémon X and Y.
The Pokémon that you receive from Shauna has a fixed OT, ID Number, Nature, Ability, Level and Nickname.
If you really want a Froakie with a different name you could always breed the Froakie Shauna give you with any Pokémon in this Egg Group or trade for another one online.
If you plan on Evolving Froakie into a Frogadier and then into a Greninja you can also catch a Frogadier from the Water Type Friend Safari as an alternative to breeding or trading.
Hope I helped :)