You should file an adjustment of status application for your wife so that she can receive a conditional green card. An experienced attorney can help you fill out the paperwork and help you gather evidence that your marriage is in good faith. For a series of articles about adjustment of status, see the link below:
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She could have changed her name when you applied for the California marriage license and certificate. When she applies for the greencard, she can use the new name. Otherwise, she should change her name through the court, or wait until she can naturalize (get US citizenship), and change her name concurrently.
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Your question is a little confusing as to exactly what you need. If you are planning to petition your wife for permanent residency, you will need to file an I-130 and I-485. Please be aware that although the age difference should not be a problem, it does raise red flags with USCIS. So you have to be sure that you have all of the necessary documentation to prove the validity of your marriage. She can change her name at the time that the petition is filed.
If you are asking about just changing your wife's name, she would need to file a petition with the court.
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Legal disclaimer: The answer provided is general in nature and because not all facts are known, it should not be construed as legal advice. The answer does not create an attorney/client relationship. You should speak to an attorney for further information.