The Independent Police Complaints Commission have named him as 29-year-old Spencer Ashworth.
Mr Ashworth, whose last known address was in Portishead, was shot by Avon and Somerset Police firearms officers on the A369 Portbury Hundred shortly after 9.30am on Wednesday morning.
The Independent Police Complaints Commission (IPCC) is independently investigating the circumstances of Mr Ashworth’s death.
Initial information indicates officers were responding to a report of a man travelling on the M5 with a handgun and that he had threatened another motorist.
The IPCC has also been informed of an earlier incident where a similar report was received by West Mercia Police.
The vehicle stopped by police on the Portbury Hundred was a red Suzuki Swift, in which Mr Ashworth was travelling.
The IPCC say they've established that authorised firearms officers (AFOs) from Avon and Somerset Police arrived in one marked police vehicle and two unmarked police vehicles.
IPCC investigators say evidence indicates that a number of shots were fired by four officers.
What appears to be a non-police issue firearm found at the scene is currently subject to ballistics and forensic testing.
Pic: Sky News
IPCC investigators are examining body worn video footage from a number of the AFOs.
The IPCC is appealing for any other road users who may have captured any part of the incident on their dashcams or helmet cams to share it with investigators.
IPCC Operations Manager Mel Evans said: “We are conducting a thorough and detailed independent investigation into the circumstances surrounding Mr Ashworth’s death.
"We have made positive progress and are continuing to build a detailed picture of what happened.
"We have made contact with Mr Ashworth’s family to offer our condolences and explain our role and will ensure they, Avon and Somerset Police and the Coroner are kept updated as the investigation continues. Our thoughts remain with all of those affected.
“If anyone witnessed events who has not yet come forward we would be grateful to hear from them.”
The IPCC received referrals from West Mercia Police and Gloucestershire Police in relation to how they dealt with information received from a member of the public prior to the incident near Portishead.
The member of the public made the report to West Mercia Police.
This information was then passed to Gloucestershire Police.
After careful assessment the IPCC says they will not investigate the actions of either force.
Pic: Sky News