Why would her name be changed? What the hell is wrong with Dazzler? I love Dazzler, it doesn't date her at all. Maybe the Disco Dazzler, but she doesn't exactly go by that anymore. Not that she ever really did, barring the Dark Phoenix Saga.
Dazzler needs a good story arch where she plays a prominent role, she's always a background character and usually fails to do anything significant or gets compromised (Malice/Gambit). And she needs a good costume design that's more reminiscent of her "Pryde of the X-Men" and Jim Lee redesign, than that stupid silver Disco costume. Dazzler has always been, to me, a short-haircut girl. I think an update of the Jim Lee design (below) with a cut sort-of similar to Frenzy's but blond up top and pink on the bottom would set her apart, and distinguish her from the other blonds. Maybe give her he eye paint from her original costume but that's it.
http://www.comicvine.com/images/1300-3092067/ <- Dazzler's best costume... ever. Thank you Jim Lee.