The explanation of the origin of Sam Gamgee’s name from Tolkien’s perspective is very simple. He adds that Sam is a rustic character, too. But the philologist doesn’t stop with his own answer. He takes advantage of the opportunity to dive into the etymology of the real-life Gamgee family, too, and it turns out that the real Gamgees are much more prestigious than their bucolic counterparts in Middle-earth — at least before the whole “save the world from utter destruction” bit.
In the real Gamgee’s original letter, the fellow explains, “I know it’s fiction, but it is rather a coincidence as the name is very uncommon, but well known in the medical profession.” That last bit about a renowned medical Sam Gamgee clearly piqued Tolkie’s interest, and in his response, the author follows up on the point. After explaining his reasons for naming his character Sam Gamgee, he adds that “I know now, that ‘Gamgee’ was shortened from ‘gamgee-tissue.'” This is a surgical dressing invented by none other than a J. S. Gamgee in the 19th century. Tolkien elaborates that he knows the inventor died in 1886, and a man who he presumes to be his son had died just a few weeks before their correspondence after years spent as the Professor of Surgery at Birmingham University.
“Evidently ‘Sam’ or something like it, is associated with the family,” Tolkien adds, “though I never knew this until a few days ago, when I saw Professor Gamgee’s obituary notice, and saw that he was the son of Sampson Gamgee.” While the overall comparison is uncanny, Tolkien does use the italics to clarify that his character is Samwise, not Sampson or Samuel.