A. The two names are certainly connected. Dod means “beloved”, and David is a passive participle from the same root.
David was the youngest son of Jesse (Yishai) and was anointed by Samuel after the older sons had all been rejected. He was “ruddy, with beautiful eyes and goodly to look upon” (I Sam. 16:11-12).
AH Sayce suggested in 1887 that David was not necessarily a personal name but a title or office like Pharaoh and Avimelech, and that the real name of the David we know was Elchanan.