Γύλιππος (Gýllipos) in Gerhard Köbler’s site is all I get, and all it says is “origin unclear”.
It does indeed look like a compound of gyl– and hippos “horse”. There is no gyl– word in attested Greek. There are the diminutives gyl-arion and gyl-iskos referring to kinds of fish; and there is the noun gylios, referring to a long-shaped satchel (Aristophanes), or to a hedgehog. Aristophanes also has the word gyliauchēn “gylios-necked”, meaning “long-necked, scraggy-necked”. gyliippos > gylippos could possibly be a “gylios-necked horse”, or someone associated with them.