A diminutive of the female given name Abigail, from Hebrew, also used as a formal given name.
"I spose you want to be a cattleboy," drawled the multicolored beard whose name was Carrol Day, a curiously feminine name, thought Martin, not yet acquaintanced with the bearded Marions, Fannys and Abbys of Texas who, saddled by their unthinking mothers with dainty names, built savagely masculine frames of character. 2002, Annie Proulx, That Old Ace in the Hole, →ISBN, page 81:
A diminutive of the male given name Albert, from the Germanic languages.