What can I do if I have my wife's name on my bank account for information purposes only and not as a joint owner?

I am unaware of any "info only" nomenclature on a bank account. If you put her name on it, she is probably a joint owner, and has the legal right to remove 50% of the deposits and will inherit the account outside of probate if you predecease her. You state she has no signatory rights, which suggests to me that this might be a trust account in which you have sole ownership and can revoke it by removing all the deposits at any time. She only obtains funds if you predecease her.

Your wife would be a "co-owner" of the funds in that account if accumulated during your marriage as California is a community property state. If the money was yours prior to marriage then the money is presumably yours. Before concluding with that however there exist rebuttals to that presumption that would require time with an attorney and additional facts.

I am unsure of your question. If the bank says she is not a co-signor, then she cannot remove funds, so there would be no problem. However, if you are in the middle of a divorce any monies earned during the marriage are community property and subject to division by the court, upon a court order, the characterization of property as community or separate will not happen until you get to a final trial date or come to a final Judgment with a Settlement Agreement (not just temporary orders at a hearing). This is the reason that the automatic restraining orders listed on your Summons go into effect immediately (neither of you may use, dispose of, encumber any assets except in the ORDINARY purposes of everyday life (normal living expenses) without the court's approval.

If the money in that account was earned and/or acquired during marriage she is entitled to one-half of it. If it was received by gift or inheritance she is not. If it is part earnings and part gift/inheritance, she is entitled to one-half of the earnings part.

Read the agreement you signed with the bank - it will define the positions you and your wife have with respect to the account. Move the money out of the account into one in your name only.