There is really no reason to call him "The Tramp". He's "the tramp", perhaps, and certainly a tramp. This would more appropriately be titled Tramp (The Tramp's Story).
Talk about it here.
One Christmas, the Tramp saved up enough money to buy himself a bottle of champagne. It was knocked out of his hand by a passerby before the tramp could drink it. The Tramp wished to end his life and stood in the middle of the road to be hit by a bus driven by a woman called Rita. He was saved by the Seventh Doctor. The Doctor claimed to be trying to get one over on his enemy, Death.
The Tramp later encountered the Auctor, who told him why the Doctor saved his life. If the bus had hit the Tramp, then Rita would have blamed herself for his death and commited suicide. The Auctor informed the Tramp that his life being saved distrupted the Web of Time. (PROSE: The Tramp's Story)
The Tramp was later removed from history by the Doctor to protect the Web of Time and was placed in a zeppelin that was endlessly looping through the heart of the Time Vortex. There he recounted the story of his time with the Doctor to Charley Pollard. (PROSE: Repercussions...)