At an untowered field, saying the airport name at the beginning and end of each transmission is standard phraseology.

If anything, the tail number does not matter nearly as much. A plane with auto land presumably already has ADSb out (almost certainly 1090ES), is squawking 7700, and is probably already IFR anyway. As in this situation, the controllers knew well in advance they had an emergency inbound and who it was. At an uncontrolled field, I need something to tag (robotic "bravo-romeo" is plenty) and a relative position. Bonus if it does the math and predicts landing time, which it does.

Frankly, it should know (like I have to) if it's going to auto land at a towered field or uncontrolled, and adjust as necessary to those circumstances.

It's an outlier because typically the comms cycle is very fast and only a single cycle. The radios are also quite bad and there isn't room for errors that you'd normally correct naturally in the context of a longer conversation