This can be tough because parameters aren't meant to be an "either/or" option. I would try making both parameters a string. The first one is a drop down that selects "Date" or "Name" option. The second one is an empty text field where they can type in anything they want. If they selected Date, then they need to enter a date. If they selected Name, then they need to enter a name.

In the record selection formula you need to use conditional logic to say, If Date is selected, then test on the Date field. And the same for Name. The pseudo code would be

if param1="Date" then
   CDate(param2)=datefield
else
   param2 = namefield;