On one of the later episodes of The Bob Newhart Show, one of the
Darryls ends the show playing a piece of classical music on a rotating
grand piano. What is the name and composer of this piece of music?

I have not been able to find the answer to your question, but I
remember the episode (it's hard to forget the Darryls in white
tuxedos!)

A note for other Researchers: the show involved was not "The Bob
Newhart Show" (that was Bob's earlier series, with Suzanne Pleshette.)
This show was entitled "Newhart."