In California we have laws against Cyber-stalking (Internet only),
Yes ... but, it is hard to say whether the elements of the related statutes have been met.
or you can file a Civil Harrasment suit (you should print out and document the emails, slander, etc. have family and friends forward them to you) after you have made it clear to him that you want it to stop and that you have not invited or encouraged the guy.
Well l... since it's a former dating relationship, it would be a DV TRO, not a CHO. No great difference in content, but, the application should be on a sliding scale or free, and enforcement would require an arrest if it were issued and there was probable cause to believe the suspect violated the order (though probable cause can be waffly when the contact is made electronically and the suspect denies it).
At the same time you should also make it clear to him that you want him to stay away from you. Document, document document. Get a binder ready!
If only more people would do this!
If he ever comes to see you, is trying to find you, shows up at your work, or sends you anything, call the police non emergency line and get a police report. Depending on your local department, they might whine, but you insist on getting it documented. If he surprises you by showing up somewhere to see you, call 911.
If he is not doing anything, the police may not respond. If she is alleging stalking, they probably will. However, the OP reports the contact is electronic at this point, so the level of reporting would likely be limited to misdemeanor harassment via electronic means (per PC 653m). And I don't know that 9-1-1 is the appropriate call to make if he just shows up somewhere ... but, if she feels afraid because of something he says or does, sure. Otherwise, no.
If you decide to file a civil harrassment suit, you can file for a restraining order and the judge can order him to stop mentioning your name or referring to you on the Internet along with the no-contact order.
Beyond the civil case, the DA can file criminal charges against him if it continues.
Make sure you have your ducks in a row. You'll have to show several times he's ignored your demand to stop (Remember do not encouraged him. Don't reply, don't name call, ignore but document) You do NOT have to take it.
A CHO/TRO is not going to state that the protected person cannot mention the name of the restrained party. It will give certain conditions like not contacting or harassing them, staying away from them, etc. Sometimes internet postings - such as to Facebook - can be considered indirect or third party contact in violation of a CHO/TRO/CPO. Sometimes. However, it has been my firsthand experience and my understanding from other jurisdictions that these indirect communications can be tough sells to a jury. Trying to convince a jury that a posting to FB or a message to someone else about the protected person without a request or expectation that the protected party be contacted can be a tough sell, indeed.
A CHO/TRO will prohibit contact. Whether the OP can get one after months of nothing and then one lengthy email is questionable. She would also have to show that the actions give good cause to fear for her safety as a result of his actions.
As I previously mentioned, unwanted harassment via email, text or phone can be a misdemeanor criminal offense per PC 653m. A report or two for that might lend credibility to an application for a DV TRO, but, it's still no guarantee that a TRO would be issued. And if the actions become frequent again, a case for stalking might be able to be made ... maybe.
I have yet to ever see a TRO or a CHO order a defendant not to even mention the protected party online. I also have my doubts that such a muzzling order would even pass Constitutional muster. I have seen similar restrictions in the context of broader conditions of parole or probation that restrict internet access and the like, but, as part of a TRO or CHO (which are civil documents, not criminal), never.