or does anyone know what that part is called?
Yes, Andrew, it is called the "downtube frame gusset". It adds a bit of extra bracing for strength on Thorn frames capable of using a suspension fork (i.e. the Nomad Mk2).
I would treat the rust with a little phosphoric acid to convert it to an oxide, then treat it with paint, wax or oil as desired. It is open at the bottom so should drain rather than trap water in the future.
My Nomad has this gusset, as does another bike. My Nomad is still unrusted, but another bike came to look a bit like yours (I purchased the frame used and it had been pressure washed, causing water to blow up into this area). I treated it as mentioned and it has given no further problems.
Best,
Dan.