I too have heard it pronounced and typically pronounce it "die-neh-seh" or "die-neh-zeh". I have no idea whether the "s" or "z" sound is correct, nobody has commented, regardless of which I use. It seems the important part is that it's three syllables, and the "e" at the end is enunciated (i.e. it's not silent).
man, this question comes up a lot! i think someone resurrected an old thread not long ago on the same thing. what's funny is that there are always a lot of varying answers. the one above is from wikipedia, and while it may be accurate... most people will read/ennunciate it wrong.
so..... pronounce it as: "die-ih-nay-zay". that is the most phonetic spelling i can come up with. note that the second syllable is soft/short, more of an accent off the first syllable. at this point, dainese should put a recording of their name on their site or something.