Hayley Logan, a 21-year-old woman from Stow, died on Saturday following an early-morning fatal collision on the A7, just north of Galashiels.
Police say her Peugeot 107 car left the road resulting in her being seriously injured.
Hayley was taken to Edinburgh Royal Infirmary but later died following the crash at 3.30am on Saturday.
Officers closed the road for ten hours while investigations were carried out.
Sergeant Gary Taylor said: “Our thoughts and sympathies are with Hayley’s family at this time and we continue to investigate the full circumstances surrounding this incident.
“If you were on the A7 at Torwoodlee Golf Club in the early hours of Saturday morning and remember seeing anything suspicious then please contact police immediately.
“In addition, anyone with any further information that can assist with this investigation should also get in touch.”
The British Journal Editors and Wire Services