I once had a classmate with this name (though she spelled it
Murielle), and I always called her Mur. I guess this could be passable in
America as well. :) Other nicknames I can think of are Muri and Mury, though the former might remind one too much of
Suri Cruise.
And last but not least, these would be possible as well: Riel(le) and Rie (spelled as Ree, if desired). :)