I changed my last name in NJ. It wasn't due to marriage but I went from 1 last name to 2 last names, no hyphen (got rid of my dad's last name, took my mom's and grandmother's last names since they raised me). Legally there's no issue. The Superior Court of NJ approved it no problem, the NJ Bureau of Vital Statistics changed it no problem, and Social Security accepted it no problem.

The only place you may run into trouble is the NJMVC (DMV). I researched before I went and found out that legally there's no issue but DMV workers like to give people trouble with unusual last names (double-barreled, spaces, apostrophes, etc) a hard time. They gave me a hard time because they said it all wasn't going to fit on the license (spoiler alert: it did). They tried to tell me that only the second last name was my last name and that the other last name was a second middle name. But like the other poster said, they only allow one middle initial so they were basically going to just omit one of my last names. I basically told them they don't get to tell me that my last name is my middle name. The names aren't in English so they told me fine, I have to prove that the name has been used in the past as a last name or show them some kind of legal documentation that it is part of my last name. You don't have to do any of that, but for the sake of getting them to do it I just showed them my grandmother's last name and the application for my name change where I listed both under the last name section. Finally they said they would try to put both in the last name section but that it wouldn't fit. I knew it would so I told them to try. It did. The only thing is NJ licenses don't allow spaces or apostrophes for any reason. From articles I've found online it's a really common problem with Italian and Hispanic/Latino last names. ON NJ licenses Italian names with apostrophes lose the apostrophe (D'Amico becomes Damico). Hispanic/Latino people often have 2 last names and the names become combined on NJ licenses (Garcia Hernandez becomes Garciahernandez). My last name lost the spaces on the license. The only way to have the last names appear separately on the driver's license is to have a hyphen. But legally your name will still be without the hyphen. It's really hasn't been a problem since it's a known issue for NJ licenses. They're working on fixing it to comply with the federal REALID act. Legally there's no issue and my name still has the spaces.