To assign the Tester to Test Run, Open Test Run > Click on 'Execute'
Step 1: Expand 'Bulk Actions' menu
Step 2: Click on 'Assign Tester'
Step 3: Select 'Test Case/s' using the checkbox
Step 4: Type Tester's name in 'Assign selected To' and select suggested Tester's name to assign the Tester.
Here is the link to help documentation.