The Moat is a section of the Soham Lode, the main river that runs through Soham, where the name "The Moat" came from is uncertain, although there is nearby an old house by the name of The Moat Lodge, so perhaps this part of the river used to supply a Moat that once surrounded a building nearby, or was part of the Moat itself,  there is evidence elsewhere in the vicinity that this maybe the most plausible answer.

The photo on the left shows the Moat taken from College Road bridge looking along towards Stone Bridge, College Road is a short lane running from Clay St towards Soham Village College. On the right shows the Moat taken from the same location but looking towards the Lions Mill.