Griever is one of the bosses on the final battle sequence of Final Fantasy VIII.
You get the option of naming (or using the default name) Griever mid-game, when Rinoa asks about the lion ring Squall uses.
There is no evidence of Griever existing before he is used by Ultimecia.
Given the mind-games that take place in the story, it is no wonder if Squall's mind could create a GF.
The ingame flavor text for Griever reads:
In Squall's mind, the strongest GF ...
So it seems like a bit of Chunibyo by Squall's part.
The wiki on Griever speculates that this is indeed true:
Griever's true nature is made more explicit in the Japanese version of the game where Ultimecia claims to summon the one entity Squall views as the most powerful whose power would only increase the stronger Squall envisions it. This means that this manifestation of Griever is powerful purely because of his importance as a symbol in Squall's mind, and could even be seen as Squall needing to overcome a part of himself to win the battle.
There we have a hint that Griever did not exist before that final battle. So how did Griever come to be?