I moved from CA and for private resons I need to change my name. I fell into debt with some people that would like to injure me. I moved for my own safety but now I feel changing my name would be smart to insure I don't have anymore threat. How can I change my name here in PR when I have a CA birth certificate.

I'm not sure about in Puerto Rico, but I know in the U.S. a judge will not grant a name change in order to avoid debt. That is fraud. Now, because you say there are people that want to harm you, I'm going to go out on a pretty sturdy limb and guess that the debt you are in is not from a credit card (or the like). My best advice is to get a lawyer.