Paul Donaldson, from Chelmsley Wood, was hit by a car between Ashted Circus and Curzon Circle on Lawley Middleway at about 02:30 BST on 25 September.
The 42-year-old was taken to hospital but died as a result of his injuries later that day, West Midlands Police said.
Two men have been arrested and released on bail, the force said.
More on this and other stories from Birmingham and the Black Country
A 29-year-old driver of a Vauxhall Vectra was arrested on suspicion of causing death by dangerous driving and failing to stop, while a 78-year-old driver of a Fiat Panda was arrested on suspicion of drinking and driving and failing to stop.
West Midlands Police appealed for witnesses to contact them.
A man who died after being injured in a hit-and-run crash in Birmingham has been named by police.