Legal Question in Family Law in California

It is not really going to make much difference as long as you use the same case number. But if you want to be precisely correct, you use the same name in the caption of the case as always, but identify yourself and sign your name as you currently name yourself. If you are using your name in a context where you think it might cause any confusion, just use "Current Name (formerly Previous Name)." It is also perfectly alright to just use "husband" and "wife" or "petitioner" and "respondent" to avoid confusion.