Her family were expected to travel to Scotland today to finalise arrangements to bring her remains home.
The 25-year-old, from Coleraine, Co Derry, was studying medicine at Newcastle University in England having previously studied in Edinburgh.
Ms Finnegan -- the daughter of Owen Finnegan, a retired doctor -- had a twin sister, two other sisters and brother.
Two of the other climbers who died were named as 24-year-old Christopher Bell, from Blackpool, and Tom Chesters (28), who was living in Leeds.
The four bodies, two men and two women, were recovered following a major search which included two mountain rescue crews and police dogs.
A friend of Una, who was with her when the group were swept away, survived unscathed. He gave a brief statement afterwards: "On Saturday, January 19, 2013, five of my friends and I were descending a mountain in Glencoe, in an area known as Church Door Buttress, when the party was swept away by a snow avalanche.
"It is with much sadness and deep regret that some of my friends have died as a result."
The victims were said to have been carried about 1,000ft down the 3,772ft mountain.
It is believed the friends were descending from the peak when the entire slope began to move. Other climbers raised the alarm.
The woman survivor, aged 24 and from Durham, remained in a critical condition in a Scottish hospital last night. She had suffered serious head injuries. The male survivor contacted police after the avalanche.
East Derry MLA David McClarty, a friend of the Finnegan family, said: "My sympathies go to the family of Una and all the families affected by this tragedy."
Mark Diggins, co-ordinator of the Scottish Avalanche Information Service, said weather conditions were fairly dry and there had been little snow over the last four days. He said it was possible for a single climber to trigger an avalanche
Andy Nelson, deputy head of Glencoe Mountain Rescue, said: "It would have unfolded in a split second, they would have felt the snow moving and then have been travelling at a speed that was impossible to stop.''