You have left out certain important information, namely have you assumed your husband's name for other things like your driver's license, social security card, passport, credit card accounts, etc. This would show an intent to have your last name changed to that of your husband's.
You may file a complaint with the court in the county where you live to seek court's permission to file a name change. The procedure is spelled out for those who want to do this on their own at the New Jersey's online court's website, which I included below:
http://www.judiciary.state.nj.us/prose/10551_namechg_adult.pdf
It is also possible that you may be able to apply for a correction on your marriage certificate. You can try contacting the NJ Dept. of Health's Vital Records Office and see if there is a procedure to modify the marriage certificate based upon a mistake that was made on your initial certificate, although they may question why it took twenty years to catch it. The NJ Vital Statistics website does mention corrections on birth certificates but not for marriage certificates, however, you may want to give them a call or send them an email.
Answered on Jan 21st, 2016 at 2:23 PM