Lisa Saville died shortly after being found with serious head injuries in City Lane, Wheatley, in the early hours of yesterday.
The 19-year-old is thought to have been on a night out in Halifax town centre earlier in the evening.
Two people arrested yesterday on suspicion of manslaughter - a 19-year-old woman and a 24-year-old man - have since been released without charge.
A 42-year-old man remains in police custody and is understood to be the taxi driver detectives sought yesterday in connection with the incident.
Lisa is believed to have travelled to City Lane after getting into a Hackney carriage-style taxi with two other people at a taxi rank on Waterhouse Street, Halifax. The taxi is described at white and had a sliding door.
Detectives are still investigating what happened to Lisa and how she got hurt.
Lisa was a student at Holy Trinity Senior School and Calderdale College and is believed to have worked at the Hairy Lemon on Lord Street in Halifax town centre.
Her father, David Saville, runs DS Security which provides door staff for several of Halifax’s bars.
Family friend Debbie Nicholson described the teenager as “beautiful, inside and out.”
Her son David grew up with Lisa and the pair were close friends until David lost his life in a car crash last year.
“They were like brother and sister,” she said. “Lisa was a beautiful, beautiful person, one of the nicest people you could meet.
“Nobody could say a bad word about Lisa. She was really popular, everybody knew her.
“She didn’t have a bad bone in her body.”
Facebook has been flooded with tributes to Lisa from her many friends. They include from Kathryn Roberts: “You said the last words you were ever guna say to me last night. At least I got to say love you. RIP Lisa, love you babe x”
Police are urging the taxi driver or anyone with information that may help their investigation to contact Calderdale CID on 0845 6060606 or CrimeStoppers on 0800 555111.