Take a branch with a few leaves on it to a local nursery, garden center or local botanic garden if you are lucky enough to have one, or county extension office. Only people familiar with So Cal, NM, or AZ landscape business would be able to guess. As a silly northerner, any guess I made would be way off, and I'm a better than average guesser in the what's my plant game. Nothing I can think of would survive full south sun exposure in AZ, hell I wouldn't survive it either. I only visit AZ in middle of winter, and I still feel like it's hotter than my summer.