I’m asking, because people call him “Rumpel” or “Mr. Stiltskin” and Shrek calls him “Stiltskin.”
The credits for the film list his name as "Rumpelstiltskin" (all one word)
As does the DVD box cover for the film.
His desire to go by "Mr Stilstkin / Rumpel" may be a call-back to earlier myths where going around telling people his full name would be undesirable.