blacksmiths last names were base on their work like green for coppersmith or just smith. i can assume the Tanner or Foster: leather maker and what ever foster parent were called then. However, Did prostitutes have last names base on their occupations?
To make the subject line more precise, they had last names (if their cultures had surnames): you want to know about occupational bynames that specifically refer to prostitution.
I don't have a comprehensive knowledge but I can at least cite some examples.
Talan Gwynek (Brian M. Scott), "Late Period Feminine Names from the South of France", "The following names appear in Appendix B, Lists of Prostitutes, of Leah L. Otis, Prostitution in Medieval Society (Chicago: University of Chicago Press, 1987)." It looks like a lot of them used surnames typical of the culture, but "la Puta" is cited to 1521. I also wonder whether a few names that refer to "ewe" might be euphemisms, and "la Garacha 1514 'plowing field' (or from garcha 'ewe')". (BTW, "period" refers to the period of the Society for Creative Anachronism, up to 1601, or in some cases 1651.)
Juliana de Luna (Julia Smith), "Names from Sixteenth Century Venice", notes "the most common occupation for women discussed here is prostitute" (the source book is Working Women of Early Modern Venice (by Monica Chojnacka, Baltimore: Johns Hopkins University Press, 2001)), and it mentions "Meretrice (prostitute)".
Juliana de Luna (Julia Smith), "Arabic Names from al-Andalus: Feminine Bynames Found in al-Andalus (nisba and laqab)" cites al-F{a-}siqa as "prostitute". Juliana doesn't mention her source, which is highly surprising (the Academy of Saint Gabriel, and she, have high standards in scholarship); if anyone would like to know, I can ask her.
Reaney and Wilson, A Dictionary of English Surnames, s.n. Trugg, Trugge, says "c.f. early modern English trug 'prostitute'", but doesn't specifically say that's the origin (and "c.f." implies it isn't), but gives no etymology. Trull is also a surname in R&W; it means 'slutton, drab', but "drab" at least modernly can be defined as "1. A slovenly woman; a slattern." or "2. A woman prostitute." (Alas, R&W have headnames only of the names themselves, not concepts or categories. Words I can think of like "whore" are missing or have some other derivation; e.g., "Trollop", as in the famous mercenary, is from "troll valley.")
Certainly would say something about the ancestry of Joseph Dalton Hooker.