I have actually read Richard Asher's book, surprisingly. (My wife, who is a doctor, gave it to me for interest - it is very readable. I recommend it!.)
It seems that the fictional(ised) character is spelled Munchausen, while the original, real, person was called Munchhausen.
I looked it up as I had a vague memory of having seen both spellings before. Asher seems to have picked the fictional version (understandably) for his syndrome.