Legal Question in Family Law in California

No. If you want to push the issue, however, a new live-in partner is a "change of circumstances" that would allow you to request review and possible adjustments to the current custody order. Once you file an OSC re: custody modification you can propound discovery to obtain her identity. So if you are willing to "go to the mat" about it, eventually you can get the information. Perhaps if you politely but firmly let your ex know that "this can be done the easy way or the hard way, but ultimately he will have to provide the information" he will see the benefit of providing you the information and reasonable assurances about the character of his new cohabitant rather than going to see a judge about it.