Copy and paste are not the best steps to use here. Not only are you limited to the contents of a single field for your find criteria, if the user has previously copied data to the clipboard, the script replaces that data with data copied by this script. It's better to use other means to move your data such as using set variable to copy the data into a variable and then set field to set a field to the variable's value. That completely avoids the clipboard and you can use two variables, one for each field.
Set Variable [$caseNumb ; value ; db::case number ]
Set variable [$caseName ; value: db::case name ]
Enter Find Mode
Set FIeld [db::case number ; $CaseNumb ]
Set Field [db::case name ; $CaseName ]
Perform Find 
For more examples of scripted finds: Scripted Find Examples
when i use the set field command, just as you typed it, i get an error that "an operator is expected here"
When Setting up Set Field, there are two Specify buttons that must be clicked. To get Set Field [Table::Field ; Expression], add set field to your script and click the first button (specify target field). Select Table::Field from the list of fields. Do not click the specify button next to the repetition box. Click OK to close this dialog box. Now click the lower specify button (calculated result) and create the expression to the right of the semicolon (;). Do not try to type in the semicolon.