Name for "uniformly polynomial" subclass of XP?
I don't think this subclass of $\textsf{XP}$ has been studied in the literature (and given a name).

One reason why researchers might shy away from studying this subclass, is that it is not closed under fpt-reductions (and so one would have to deal with an 'annoying' new type of reductions). This is because fpt-reductions allow the parameter value to blow up superpolynomially (as long as it is bounded by some computable function of the old parameter value). To get a restricted notion of fpt-reductions under which your subclass of $\textsf{XP}$ is closed, you would need to add the restriction that fpt-reductions require the new parameter value to be bounded by some polynomial of the old parameter value.