Louis Watkiss, from Sutton Coldfield, died on Friday evening after an incident during an activity at the SnowDome in Tamworth.
A spokesman for Staffordshire Police said: "Following Friday’s tragic incident at the SnowDome in Tamworth, we can now confirm that the 12-year-old boy who lost his life has been named as Louis Watkiss from Sutton Coldfield.
"Police were called at 6.40pm on Friday (24 September) to reports that a child had been seriously injured at the SnowDome.
"Officers attended the location, along with ambulance crews. Sadly, Louis, died of his injuries shortly afterwards.
"Louis’s family are being supported by specially-trained officers. We would ask everyone to respect the family's right to grieve in private during this extremely difficult time.
"Staffordshire Police is continuing to investigate the circumstances with support from the Health and Safety Executive.
"Louis's family do not wish to issue a tribute at this time."
The SnowDome was closed throughout the weekend as an investigation into the 12-year-old's death was conducted.
Martin Smith, Chairman of SnowDome Ltd, said the centre will cooperate fully with investigators.
"The directors and all of the employees extend their heartfelt thoughts and prayers and condolences to the family and friends of the young boy," he said.
"For an evening’s activity to end so tragically is almost beyond belief and our sorrow is deeply felt.
"The company is in full co-operation with the investigating authorities and is providing complete and absolute assistance."
Mr Smith added the centre will remain closed until investigations have finished, "but hope to be able to update you on the position in the very near future".
A West Midlands Ambulance Service spokesman said: "On arrival, crews found a boy who had suffered very serious injuries.
"Staff worked on him providing advanced life support, but sadly, despite all of the efforts it was not possible to save him and he was confirmed dead at the scene."