To assign the Tester to Test Run,
Step 1: Open Test Run
Step 2: Click on 'Show Execution Results'
Step 3: Click 'Assign Tester'
Step 4: Select 'Test Scenarios' using checkbox and type Tester's name in 'Assign selected To' and select suggested Tester's name and click 'Submit' button to assign the Tester
Here is the link to help documentation.