The Greek god of mischief would probably be Hermes, the messenger god who is also the god of travelers, liars, thieves, and orators. When he was only a baby, he stole cattle from Apollo.
Hermes, who is also the God of messengers, theives, buisness and travleres
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Hermes.
Hermes
Loki is the God of mischief
Diana was the Roman God who was the guardian of wild beasts, horses, and domesticated animals.
The Greeks did not have a particular god or goddess who personified mischief. I think, however, that you are probably thinking about Pan, the half-goat god of the Wild. His Roman counterpart was Faunus.Similarly, satyrs and fauns are generally portrayed in modern culture as being raucous and mischievous, though the Greeks and Romans didn't necessarily intend for them to embody that.