He was named for an old family relative, but by the time he was a toddler, his parents realized 'Stefan' just didn't suit their little boy, so they started calling him by his middle name: Thomas. 

Tom doesn't remember his childhood--not the way it really was. Because when he was 12 years old, he lost his parents, and went to live with his father's cousin, Zach. . .and then he met Damon. The vampire recognized his little brother's face on this child, and decided he would seize the opportunity to recreate the relationship he'd lost, despite Zach's protestation. So all of Tommy's memories of a happy childhood with loving parents were overwritten with compulsion, replaced with a story about a cruel drunk of a father, and a spineless mother who stood by and let it happen, and an older brother who'd tried to protect him. 

For five years, Tom lived under this belief. He also developed a drug addiction in his first year of high school, which led to Uncle Zach pulling him out of school and sending him to rehab, then homeschooling him for the latter half of his sophomore year. By the time junior year rolled around, Tom Salvatore was the new kid, even though he'd lived in Mystic Falls for years at this point; no one remembered the awkward loner boy from freshman year. This was also when he (officially) met Elena Gilbert; something that would change the course of his life in ways he could've never imagined. 

With both of them being human, Tom and Elena discovered the supernatural together. They both had their worlds turned upside down by the revelation of vampires, as well as learning their families weren't what they thought they were. Then. . there was the matter of them being doppelgangers. 

Nothing in Tom's life turned out the way he planned.