After Dad died his car automatically became Mum's property even though she didn't drive (he didn't leave a will). I took on responsibility for it and I became the registered keeper. I dealt with the change of keeper as you would for any other change of ownership.
Obviously I didn't have to deal with DVLA after Mum died, but I found that, generally, the bigger places that you'd expect to be a bit impersonal turned out to be some of the best to deal with. Tax office and DWP were brilliant and I'm not surprised to hear that DVLA are also good. Council tax, however, has been an ongoing nightmare.