Variant of Farrar. Compare Margrett Farrer 1585, Katheryn Varey 1591 in IGI (Kendal Westm); John Vary 1663, William Farrar 1675 in York Freemen's Register (York); Robert Farrah 1665, Anne Varo 1708, Jno. Varey 1716 in IGI (Barwick in Elmet WR Yorks); John Farrah 1689, John Varey 1696, Tho. Varah 1724 in IGI (Leeds WR Yorks).
Perhaps from Middle English varay, verrei, verri, werr(e)i (Old French veraie, varei, Anglo-Norman French verri) ‘truthful, upright, trustworthy’. As Redmonds Dictionary of Yorks Surnames points out, the NR Yorks name appears to have a different origin from that in (1), while the 16th-century spellings for the Rotherham name (implying a long vowel or diphthong) also look more like this name than that in (1) where a short vowel is more usual.
However, the two names may easily have been confused, especially in S Yorks.