"Minne" is the
Dakota ("Sioux") language word for "water", though it may be more correct to spell it as
mni.
The "haha" in Minnehaha does NOT mean "laughing", however, but just "waterfall". "Laughing water" is a so-called "folk etymology". It might "make sense" to an English speaker that "haha" would mean "laughing", but that's not what it means in
Dakota. :)
http://www.bartleby.com/61/90/M0319000.html
And of course none of this means that the word "Minne" or "Mni" was ever used as a name in the
Dakota culture.