Family name on a headstone in the graveyard in Godric’s Hollow, probably ancestors of Hannah, since wizarding families tended to live close together in certain villages after the Statute of Secrecy went into effect in 1692 (DH16).
Notable members of the family:
Rowling considered the Abbott family to be pureblood, but an inconsistency with old notes (that imply that Hannah Abbott is Muggleborn) made Rowling change her answer (JKR). She settled on Hannah Abbott being half-blood, implying that the Abbott family is both magical and Muggle.
Neville joined the Abbott family when he married Hannah Abbott (JKR).
Abbott is an English and Scottish occupational surname, for someone who works in the household or lands of a nun or priest.