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Using the father's name as a second Christian or forename follows the lead of the royalty calling their illegitimate offspring Fitz.
It should also be remembered that the young girl/woman may not have been a willing participant in the liaison with her employer or his son(s), they held a lot of hold over the young girl/woman both in terms of employment, where little may have been available in the area, and references and therefore coerced or forced the young girl/woman into sex with them.