Continuous documentation at the DMV in NJ is only one of the problems with a very broken system. Real ID implementation was late in coming here. And honestly you couldn’t sell your first born for an appointment… and no admittance without an appointment. Problems with DMV funding and staffing mean waits of 3+ hours with the appointment. Many people in NJ have passports and have done perfectly well traveling on that.
I have to digress and say the problem I had with name variation came decades ago when I was married in Cambridge, while living in Chicago… this was the mid 70’s for those who remember the political climate in Chicago back then. The federal government updated my passport with my married name one way but the DMV in Chicago did it another way… could have, should have challenged it then. But this was a place when I brought a document that wasn’t notarized actually sent me out to the hot dog vendor in front of the building… yup, he had his seal tucked between the mustard and ketchup bottles. Not a place to really argue. I was happy to get my license.
When I moved to NJ a few years later some accounts read one way, some another. Didn’t make any real life difference. Federal government never had an issue… taxes, SSA, Medicare are fine. The Real ID as implemented in NJ was when the poop hit the propellers. Glad I retired… had the time to deal with documents, appointments and the waiting. I really feel for folks here, though, who try as they might just can’t cut a break!