They don't have to change the aircraft registration number. The titles "pink slip" will all change in both fleets to reflect the PHX corporate address or possibly the PIT address if the title has to show the certificate address.
NWA and DAL are all flying aircraft with N numbers from predecesor carriers. NW has tail numbers with US, NW, RC, and RW. and an occasional E or EA. Delta still has Western Airlines WA.
The registration fee is pretty low, but they have to physically change the numbers on the aircraft, and all the log books etc. So my guess is that the HP powers at US will elect to leave the N numbers alone and develop a fleet number for every aircraft. Probably a 4 digit tail number. AA has some pretty funky fleet numbers. Some are alpha-numeric.