Unsure what the name of it is, but I would call it a radiator hose manifold. Please see pics attached that the screwdriver is pointing too, that temp repair brass barb would usually be moulded plastic but snapped off.
I am looking to buy a ECU for my 2007 Mini Cooper S R56 Auto The numbers on the current ECU are DME7610011 If you have a matching CAS and keys for an ECU I would be interested in that as well