Q: Is Parselmouth a real thing or did you make that up?
A: Parselmouth is an old word for someone who has a problem with their mouth like a harelip. -
-- J.K. Rowling [RAH]
Yes, indeed; a rare ability, and one supposedly connected with the Dark Arts, although as we know, there are Parselmouths among the great and the good too. In fact, his ability to speak to serpents did not make me nearly as uneasy as his obvious instincts for cruelty, secrecy, and domination.
-- Albus Dumbledore on the young Tom Riddle (HBP13)
A speaker of Parseltongue is referred to as a Parselmouth (CS11).
From the Web
"Parselmouths" from Harry Potter Wiki