Tom

We might naturally assume that as a Hobbit, Sam would compose a rhyme about his fellow Hobbits rather than Men. However, the fact that Tom was wearing boots is raised several times in the poem, which would be a rarity among Hobbits. What's more, he's prepared to at least attempt to attack a Troll, something that would seem rather implausibly ambitious for a Hobbit. On balance, then, Tom was probably one of the Big Folk rather than the Little Folk, though this is not stated explicitly.

The reason behind this lies in the fact that Tolkien did not write this poem specifically for Sam to recite in The Lord of the Rings, but actually long beforehand. Its origins lie in a poem "Pēro & Pōdex" that goes back to 1926, and it appears in the collection The Adventures of Tom Bombadil as "The Stone Troll". Thus the explanation for the absence of Hobbits from the poem is a simple one: at the time it was written, Hobbits had almost certainly yet to be invented.

In the Shire, the name 'Tom' was typically a contraction of the name 'Tolman' rather than 'Thomas' (as for example Sam's future father-in-law Tolman 'Tom' Cotton). The name 'Tolman' does not appear to carry a specific meaning, though it can be interpreted as originating from the profession of a 'toll collector'.

In principle uncle Tim might have been the brother of either Tom's mother or his father, but Sam clarifies the relationship in his rhyme, calling Tim 'my father's kin' (The Fellowship of the Ring I 12, Flight to the Ford).

The fact that Tom appears in Sam's rhyme without any prior introduction might lead to some possible confusion with Tom Bombadil, whom the Hobbits had met just a few chapters before the rhyme appears in the text of The Lord of the Rings. The fact that both these Toms wear distinctive boots might also potentially add to this confusion (as might the fact that a version of Tom's Troll poem appears in the collection titled The Adventures of Tom Bombadil).

To clarify, the two are quite distinct characters, and the details of their stories make this unmistakably clear. Quite apart from the fact that kicking a Troll in the posterior is hardly Tom Bombadil's style, there are some more definitive points to consider. First, the Tom in Sam's rhyme explictly has a father, but Tom Bombadil is described as 'Oldest and Fatherless'. Second, the unfortunate Tom in the rhyme is also said to end up permanently lamed by his misadventures, but Tom Bombadil certainly wasn't lame when he met the Hobbits.

In fact these two characters had quite different literary origins in unrelated poems, and their shared name is no more than coincidence. 'Tom' is simply a common name in Tolkien's universe (it is also used by two members of the Cotton family, and by Tom Pickthorn of the Bree-land, and by one of the Stone-trolls encountered by Bilbo Baggins on his way to Rivendell).