Bruce - I'm not entirely certain, but I think an "entire number" is an integer.

Luis - I don't quite understand what exactly you want your code to return; do you want the name of the variable? Are there more variables than just "oee", and you need to find the one that ends with that specific integer? I don't think you can easily access the name of a variable once it's been assigned a value, so you might have to write this differently.

Does something like this help you at all?

gpo = {};
foo["a"] = {{{0, 50}, {120, 100}}, 2};
foo["b"] = {{{10, 30}, {110, 90}}, 4};
foo["c"] = {{{20, 40}, {80, 30}}, 7};
foo["d"] = {{{20, 50}, {70, 30}}, 2};
names = {"a", "b", "c", "d"};
DeleteCases[If[gpo == {} && Last[foo[#]] == 2, #] & /@ names, Null]
(*the ouput of this is: {"a", "d"}*)