As soon as I started thinking about the name Richmond, I figured it was probably originally Norman French. The French love place names with “mont,” which by normal sound changes often became “mond” in English. But without doing an etymological search first and spoiling my off-the-cuff comment, lol, I seem to recall that our modern “mound” is not cognate with mount or mont and that it once meant something like fenced fortification … in Middle English and Dutch, where it was usually spelled “mond.” Looks about the same as “mont,” but different Latin roots.
So the “mond" in Richmond could be Middle English borrowed from Dutch, and the similarity with the town of Richemont could be a coincidence. Or not. LOL.