The Ford Transit van, which was being driven by a 15-year-old boy, failed to stop for police near Moorlands Road, Birkenshaw, on June 13.
It was then driven the wrong way down the M606 where it collided with the taxi at 10.45pm.
The taxi driver and a passenger died at the scene.
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West Yorkshire Police have now named them as Sohail Ali, 28, of Bradford and Simon McHugh, 49, of Huddersfield.
Kyden Leadbeater, 18, of Bradford, was a passenger in the Ford Transit Van and died in hospital.
The other passenger in the van, a 17-year-old boy, has now been discharged from hospital.
He was arrested and interviewed on suspicion of causing death by dangerous driving but has since been released on bail, pending further enquiries.
A 15-year-old boy, who police have confirmed was driving the Ford Transit Van, remains in hospital under arrest on suspicion of causing death by dangerous driving.
Detective Inspector Paul Conroy of the Major Collision Enquiry Team said: “This is a very tragic incident where three people have lost their lives, our thoughts are with their families at this time.
“Our investigation into the road traffic collision is ongoing and I would appeal to anyone who saw the Ford Transit Van prior to the collision to come forward.
“We are keen to get any dash cam footage or any social media footage of the driving prior to the collision or the collision itself.
“Footage given to the investigation will be treated in strict confidence.
“The 15-year-old arrested on suspicion of causing death by dangerous driving remains in hospital and we will look to interview him when he is fit and able.”