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You given name can be different than your legal father's name there is nothing wrong with this. You may want to check your birth certificate and your social security card. If you names are XXXXX XXXXX both then it does not change the fact that you are legally married and it should not give you a problem. If you took your husband's last name then you can leave your name as it currently is and there is no need to try and change your name. If you kept using your step father's last name then you may want to look at legally changing your name to his last name to make things easier in the future. I suspect that it will never cause you a problem but changing your name through the court will make sure you never have a problem.
Please know that there is nothing illegal about your situation.
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