In a column entitled “An Englishman’s Name is his Castle,” from (I think) Life magazine circa the early 1970s, the author gave numerous examples of the unexpepcted pronunciations of many English family and place names. (I’m pretty sure this was before Monty Python’s Throatwarbler Mangrove bit.)
I think I had come across Featherstonehaugh before that in reading P.G. Wodehouse, whose character Ukridge has that as a middle name. And I think my father had explained that it was pronounced Fanshaw.
What I learned from the column was that different branches of the Featherstonehaugh family pronounce it differently (of course), and that while Fanshaw may be more common, other people say Festonhay or Feerstonhaw.
(What I also learned from trying to find the original article is that, without remembering, I wrote a nearly identical post here 17 years ago.)