If my maiden name is spelled wrong on my marriage certificate, am I legally married?

Question Details:

I have been married for just over 5 years. My maiden name was spelled incorrectly on my marriage license/certificate as my husband used a copy of my birth certificate that also had my name spelled wrong. I went to try to have it corrected shortly after we were married and was told that it could not be changed because it was typed right from my birth certificate. I was 19 and didn't really care at the time but now I am seriously wondering am I actually legally married?

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