Anthony Robinson, 42, from Worksop, died after the incident in Whitwell on Friday morning.
Family Liaison Officer PC Oliver Priddle said: “This incident is a tragedy for Anthony’s family and friends who have my sincere sympathy at this difficult time.
“They asked me to pass on their thanks to those who have contacted them to express sympathy. However, I would now ask that their privacy is respected.”
At around 6.30am on Friday, September 28, police were called to the scene of a collision between a green Vauxhall Vectra and a pedestrian on the B6042 at the junction of the A60 and Pennymore Lane.
Anthony was pronounced dead at the scene.
The driver, a 62-year-old man, was arrested on suspicion of causing death by dangerous driving and has been released under investigation.
Police are keen to hear from anyone with dash cam footage of the incident, or anyone that might have seen pedestrians in the area prior to the collision.
Anyone with any information is asked to contact PC Richard Howiss, quoting the reference number 18000464697, by calling 101 or via the online contact form at www.derbyshire.police.uk/Contact-Us.
Alternatively, call Crimestoppers anonymously on 0800 555 111.