Initially, it will be you, the person who makes the trust, but you should always list a back-up or multiple back-ups if you become incapacitated or when you pass away.
In a Will the role of manager is referred to as the Executor. In a Trust that person is called a Trustee. The list of back-up names are called Successor Trustees.
Picking a successor Trustee is a really important decision in order to ensure your Trust is followed and your heirs receive a timely and appropriate distribution.
Here is a flyer to help lay out the PROs and CONS of different categories of people you can nominate as your successor Trustee: