As griffin have not been proven to exist, being a creature out of fable, it does not have a scientific name.
However that is not to say that there is not archeological evidence that ancient people could have seen and mistaken for griffen remains; such is the theory of Adrienne Mayor, a classical folklorist, proposes that the griffin was an ancient misconception derived from the fossilized remains of the Protoceratopsfound in gold mines in the Altai mountains of Scythia, in present day southeastern Kazakhstan, or in Mongolia.
Griffin has also been used for vultures; Griffon Vulture (Gyps fulvus) and Andean Condor is Vultur gryphus, Latin for "griffin-vulture"
The griffin/gryphon is a mythical creature, half lion and half eagle. Since it is mythical it does not have a scientific name and does not fit into the tree of life evolutionarily or taxonomically.
The scientific name for griffin is "Gryphus." It is a hybrid creature in mythology with the body of a lion and the head and wings of an eagle.
The scientific name for chrysanthemums is Chrysanthemum spp.
The scientific name for squids is Decapodiformes.
The scientific name for cnidaria is Cnidaria.
The barracuda's scientific name is Sphyraena. =)
The scientific name for Echinoderms is Echinodermata.
Aidy Griffin's birth name is Aidan Griffin.
Becky Griffin's birth name is Rebecca Griffin.
Griffin Anglin's birth name is Griffin Inhyun Anglin.
Griffin Jay's birth name is James Griffin Jay.
Griffin Kehoe's birth name is Griffin Michael Kehoe.
Griffin Dunne's birth name is Thomas Griffin Dunne.
Griffin Cleveland's birth name is Griffin Barrett Cleveland.
Griffin Marks's birth name is Griffin Daniel Marks.
Alistair Griffin's birth name is Alistair Richard Griffin.
Antoinette Griffin's birth name is Antoinette Lee Griffin.
Archie Griffin's birth name is Archie Mason Griffin.
Arvid Griffin's birth name is Eugene Arvid Griffin.