Happened to me twice. First time was in Philly so they switched the reservation over to my partners name...and I was told not to drive. Second time was in Cleveland when I was traveling alone for work. I was denied that rental and needed to use taxis.

Both times, I had copies of my DL and passport (always keep scans on my phone, just in case), along with other forms of ID. While this was sufficient for TSA at the airport, National wouldn't budge either time.