The god Pan was called, in Rome, Faunus.
Also Sylvanus
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Persephone (Greek) Proserpine/Proserpina (Roman)Pan (Greek)Poseidon (Greek)Pluto (Roman)
Hercules is not a Greek God!!He was actually a demigod or HalfBlood which means that one of his parent (His father Zeus)was a Greek God but the other was a motal man or woman.But he is mentioned in Roman and Greek mythology. Hercules being the Roman name for the Greek demigod Heracles
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.
Pan god of the wild
Pan