Well, In this thread alone there are several people considering/buying CX-5 who also shopped BMW, Audi, etc. Obviously they have more work to do, but Mazdas reputation is already fastly rising.
It doesnt require a rename. Audi was a niche European brand like Saab before targeting BMW and Mercedes about a decade ago. Now look at them. No new name. Ten years from now, I highly suspect Mazda will share a similar story.
Again, I cant say emphasize enough that Mazda is in transition, which takes time. Wait 4-5 years before judging.