What bank to use

In usa im in California... to put my money in to save it NO I dont have any active cards.. my SO does but I dont want to be under his name. I want my own. I might use it once a month or not at all its more a savings account on my end. I am a home stay mom I dont work. I have cash laying around that I want to put it in a card. I dont want to be under my husband or with him cus I dont. For my own safety reasons.