The Scarborough and Ryedale Mountain Rescue Team – formerly Scarborough and District – unveiled its new look at a special open day.
The official ceremony was performed by Scarborough's deputy mayor, Bill Chatt, at the team's Barkers Lane base in Snainton.
As well as cutting the traditional ribbon, Mr Chatt unveiled a plaque dedicating the base to Peter Gough, a founder member of the team in 1965.
Organisers say the name change better reflects both the geographical area in which the team works and the nature of the work it does.
After the official ceremony, the public was shown around to look at the team's equipment.
The open day also featured a number of displays and demonstrations as well as opportunity to talk to team members about their work and the possibility of joining either as a full member or as a fundraiser.
There were also fun events for children, including a climbing wall and the chance to join in some of the demonstrations.
The service has been at the base for almost three years and volunteers say they are proud with what they have achieved. The team uses the base for training purposes and fund-raising events.
Press officer John Sheader said: "It was a great success despite the weather, which tried its best to spoil everything. Plenty of people came along which was great to see."
Members of the North Yorkshire Police Authority also attended.
* For more information on the team and for a list of recent incidents, visit www.srmrt.org.uk/index.php