Greek god of mischief

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.