can you change your name to your marriage last name if you're a non citizen?

Is it hard to do it or you can't? Even if you have the dream act/daca? 
We live in Illinois and me and my husband we're very excited to change my last name he is a citizen from here the United States but after googling it doesn't seem easy now that they ask for a citizen birth certificate😞 did anyone change their last names that weren't born here or aren't citizens. 

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