'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.