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Why is the feminine of Herzog Herzogin and not Herzögin (like Gräfin)?
According to Wiktionary "...umlaut usually occurs in monosyllables, but rarely in polysyllables", which fits the examples given. This is German though, so there are no rules without exceptions.
aandufrequently change toäandürespectively: Rätin, Ärztin, Hündin, Füchsin. Most google search results for Herzögin come from 17-19th century documents, so it might be an ancient variant of Herzogin.