'Trinity', especially in names, almost always refers to the 'Holy Trinity' of the Christian church: the Father, Son and Holy Spirit. Many places and organisations in the UK, particularly educational institutions such as university colleges, originally had links with the church. A place called Trinity Hall, for example, would have been connected to a church called 'Holy Trinity'. And even though there are no religious associations any more, the names remain. This is the same reason why so many educational organisations have 'Saint' in their names.

To add to what Su.Ki says: there are hundreds, probably thousands of institutions in the United States with "trinity" in their name, and it always refers to the Christian Trinity. There is a famous Trinity Church in Boston--and there is one in Boston. There are dozens of universities and colleges with "Trinity" in the name; the one I happen to know best is Trinity College in Connecticut. "Trinity Hall" is one of the famous colleges of Cambridge University in England. Google will find you thousands of "Trinity's" and hundred of "Trinity Hall." For example, I find that there is there is a college named "Trinity Hall" in New Jersey whose mission is "Educating and Empowering Girls in the Catholic Tradition." Trinity CAN mean any set of three, but any meaning other than the Holy Trinity is rare. I do not want to try to explain Christian theology, but the doctrine of the Trinity states that the Christian God is one being AND three beings at the same time. There is a diagram: http://tinyurl.com/lkjt9tn

Trinity is a group of three people or things.

It means a group of three things or people. It also has Christian religious references.