How does a person register a legal alias in California?

Referring to the discussion information - you should contact an attorney who practices in CA for assistance with your situation. While it MAY be that you will come out of it alright - your mother's notarized letter is worthless and means nothing. The important thing is that your alias is NOT the name that appears on your legal birth certificate (if you have one), and could definitely cause you problems when you least expect it. (just for instance: under the circumstances you cite, you could never be issued a US Passport)