Farrow is a hypercorrected form of Ferror (Farrar), an occupational surname for a blacksmith or an ironworker, an old name of early Medieval English and French origin. The name derives from the Middle English and Old French terms "ferrer, ferreor, ferrur, ferour" (meaning "smith"), derivatives of "fer" (meaning "iron" in French), from the Latin "ferrum". The development of the surname shows the usual Medieval English change in pronunciation (and thence spelling) from "-er" to "-ar" and "-ow" endings.
https://en.wikipedia.org/wiki/Farrow_(surname)