The Valar were named, and Tom is not one of them, but it has been thought that Tom is one of the gifted spirits of Ilúvatar, or God, possibly akin to Maiar, the Wizards, and possibly something else altogether.
Valar: Encyclopedia of Arda (beware: Lots of information!)
I am content and can live with Tom being Tom. He is what he is... He is the Eldest, the Master!
Tolkien himself is uncharacteristically reticent on the question of Tom's identity:"And even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally)."
The Letters of J.R.R. Tolkien, No 144, dated 1954
More on Tom Bombadil: Encyclopedia of Arda (good analysis of the common theories about Tom here)