What is the name for polynomially solvable optimisation problems?
An optimization problem is an example of a function problem: i.e., one where the task is to map some input to some output.  The class of function problems solvable in polynomial time is FP. See, for example, the Complexity Zoo.

(Note that there is a class OptP but that's not the polynomial-time optimization problems. Perhaps confusingly, it's the optimization analogue of NP: it's the class of functions that can be defined by taking the maximum out the outputs given by accepting paths of a nondeterministic polynomial-time Turing machine.)