Unless it’s spelled Beauxhommès, I would intuitively not pronounce the final -s. However, note that there’s no pronunciation rule for last names.
Also, unlike English, if the original name doesn’t have a final -s, putting one when referring to the family is not correct. The family of Dominique Dupont is Les Dupont, not Les Duponts, whereas Homer Simpson‘s family is referred to as The Simpsons.
In French, you can’t add an "s" to proper nouns when you use the plural. In English, talking about a whole family you would say "The Fords", but in French you say "Les Ford".