The address on your W-2 is just a mailing address. It has nothing to do with where you worked.
If your employer is withholding California tax, your W-2 will have CA in box 15, your CA wages in box 16, and the amount of CA tax that was withheld in box 17. That's all you need on your W-2.
If they are not withholding CA tax, you should ask them to start doing so right away. If you have no tax withheld during the year you will have a big tax bill when you file your CA tax return, plus a penalty for not having paid tax during the year. If they will not withhold CA tax, you should make estimated tax payments to CA. Then you won't have, and don't need, anything about CA on your W-2.
If your W-2 does not show any CA income, the state of California will not object to any tax that you want to pay to them. Note that if you become a CA resident and file a CA resident tax return, you must pay CA tax on all of your income, no matter where the income is from, not just income from working in CA.
