Contrary to popular belief, Mount David was not named after poets, like its neighboring peaks (such as Whittier, Longfellow, Poe, and Irving) were. Mount David and nearby Mount Jonathan were given biblical names.
I found this information online:
"The name (Mount David) was given by Forest Supervisor A. H. Sylvester. He also named Mount Jonathan, a mile to the west, linking the two peaks with Biblical history."
From the Bible: "The soul of Jonathan was knit with the soul of David."