It is doable if I understand correctly and here are the steps for achieving your report purpose.
I will use a simple query as an example data set for your reference.
1.Create source and datasets, in this example I skip the data sources and here is the short query for my exmaple
SELECT * FROM Table
WHERE
(ID = @ID or @ID = '')
and
(Name = @Name or @Name = '')
2.Add another dataset named Control, the query for Control is:
SELECT 'ID' as option
UNION
SELECT 'Name' as option
The purpose of creating this dataset is to provide the available values later when you need to choose either name or ID.
3.After step1, you should already have two parameters generated by system, which are ID and Name, if not, create them by yourself and go to each parameter page, DO MAKE SURE CHECK Allow blank value''
4.Create the 3rd parameter called Control, go to parameter setting page, go to Available Values, Choose Control dataset, Choose option (which is the customize column name you set in Controldataset) for both Value field and Label field
5.Go to ID parameter setting page, go to Default Values, choose Specify values, click fx, type this:
=Switch(Parameters!Control.Value="Name","")
Click ok
6.Go to Name parameter setting page, go to Default Values, choose Specify values, click fx, type this:
=Switch(Parameters!Control.Value="ID","")
Click ok
The ID and Name expression are correct, not set wrong
7.Change the parameter order to make Control on the VERY TOP, no matter ID or Name comes for the 2nd, but Control should be in the 1st place.
8.Drag and drop a table, place Name and ID. Preview the report, at this time, only Control will be available for you to choose value, choose either ID or Name to see the difference. When you choose ID, Name will be gray out, only ID light up and type any ID you want, actually, what the system does internally is passing the "" (blank value) to Name, that is why you need to make sure the Name parameter could accept blank value. Same for selecting Name
Update me if you have any run time issue