IdName[] Thing = new[] {
new IdName { Id = 0, Name = "No Selection" },
new IdName { Id = 1, Name = "Thing A9" },
new IdName { Id = 2, Name = "Thing C12" },
new IdName { Id = 3, Name = "Thing F4" }
};

MyDropDownList = new SelectList(Things, "Id", "Name",0);

<%= Html.DropDownList("MyDropDownList")%>

public ActionResult StoreValueFromDropDown(string MyDropDownList) {
        var id = Things.Single(thing => thing.Name == MyDropDownList).Id;
        // here goes the code to sotre the id
}

<input type="hidden" id="ThingId" />

$('#MyDropDownList').change(function(e){
     $('#ThingId').value($('#MyDropDownList option:selected').attr('value'));
});

public ActionResult StoreValueFromDropDown(int ThingId) {

        // here goes the code to sotre the id
}