Hi Jessica, you should consult with a real estate attorney, or maybe a family law attorney, before you decide.
It seems to me that if you're on title you are a co-owner and should be on the purchase agreement. If you're on the purchase agreement your half of the down payment would not need to be a gift. Loans are sometimes made in the name of only one of the owners, but you are correct in being concerned about who is on title. California, being a community property state, has some protections, but if you don't carefully read and understand everything you are signing you may not be protected. Hope this helps!
I am a real estate broker qualified to advise you on California real estate matters, not the law. If you desire legal advice, consult with an attorney.