The name on the birth certificate in this case is his legal name.

WHen they apply for their marriage license, they specify their new last name(s) on that form. The name can be either the bride's or the groom's current legal last name or combination of the two. You can't apparently change it to another unrelated name.

It becomes effective when the certificate is recorded.

To change it otherwise requires it to be made as a petition to the court. Info here:
http://www.courtinfo.ca.gov/selfhelp...namechange.htm

With April rapidly approaching, there is not likely time (unless perhaps he gets on it right away and the wedding is at the very end of April) to get it changed. Info here:
http://www.courtinfo.ca.gov/selfhelp...namechange.htm

I suspect they'd be better off to use their current names on the marriage license and then both petition for the unrelated name afterwards.

Whatever you choose to change the names, get a bunch of true copies made of the change (be it marriage license or court order). Lots of people will want to see this to update the names on things.