Legal Question in Employment Law in California

The mother is probably protected by antidiscrimination laws, baut the father may not be. But why tell anyone at work what the situation is? What need does HR have to know the father's name? An employer could find some other reason to terminate one of you, so do not cause any problems by revealing what is going on. By the way, I think most people would say ther was a relationship if two people got together to produce a child.

In general, unless you are in a union or have a written employment contract, you are an 'at will' employee that can be disciplined or fired any time for any reason without 'cause', other than illegal discrimination under the Civil Rights, or Whistle-blower, or similar statutes. Your goal should be to keep your employer happy with you. Fraternization is frequently against company policy [in order to prevent sexual harassment claims when the parties break up], and would be a basis for termination for 'cause'. Having a baby would seem to be clear evidence of fraternization and a 'relationship' that you disclosed when telling them of it. Disclosure of personal medical / confidential information would likely be a violation of privacy rights, for which the mother could have a cause of action. The father's claim would be less clear, but possible. The company has no access to a birth certificate unless you give it to them.