Mr Coulter died after being shot in the head as he and a friend left Jerky Chicken restaurant in Walham Grove, Fulham.
The Met said "it would appear the gunman had been lying in wait" for the pair to return to their car.
Detectives believe the gunman made off on foot towards North End road after shooting Mr Coulter.
The victim was shot as he was getting into the front passenger seat of the silver and black Renault Captur.
No arrests have been made.
A post-mortem examination has been arranged for Thursday.
Det Chf Inspr Noel McHugh said Mr Coulter's murder had "shocked the local community".
Detectives investigating the murder of a 24-year-old man shot in a suspected ambush have named him as Salim Coulter.