In California, is it legal to own a website/company that is similar to a person/university name (e.g. hillaryclintpn, stanfordrone)?

There are overlapping considerations. First, using a name that is confusingly similar to a senior (i.e., first in time) mark is considered trademark infringement. If it causes a reasonable consumer to believe that it is connected to or sponsored by the owner of the senior mark, a court would like strike it down. The two examples that you cite, by themselves, would probably earn a very quick cease-and-desist letter, and if action isn't taken, a lawsuit. However, if you were to use a mark in a way that makes it plain that the senior user does not support you (e.g., stanfordsucks.com), that would be considered "nominative" fair use, and would be allowed. There are also unfair competition laws that would prevent the usages you propose. I advise my clients to stay away from using other marks, because it inevitably weakens your own mark. Choose something that sticks in the mind of a consumer, without referring to others.