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This is just another spelling of Peter, your eponymous ancestor. Unfortunately I'm unable to reproduce the Hungarian spelling, because of the need for diacritical marks. The E will have an accent over it of the type the French call "acute" (aigu). The O has two of these strokes over it, a sort of elongated umlaut. The approximate Hungarian pronunciation would be Payteuh, with the stress on the first syllable. I think the spelling Peto is more common than Petho, which is an old-fashioned spelling. The combination TH no longer exists in Hungarian, except in the spelling of surnames, such as Horvath, Toth and Nemeth (all needing diacritical marks over one vowel). Try typing your name as you write it into your search engine and you'll probably find some Hungarian sites with your name written with all the Magyar trimmings.
By the way, the forename Peter is spelt as in English in Hungary today, plus an accent over the first E. There is also a famous Hungarian surname, Petofi, which is your name plus a surname ending.

If they come from Hungary , Could they be a variant of the first
name Peter, like the surname of the hungarian poet PETOFI that means "son of Peter"?