This really bugged me for a long time. Because it seemed so hard to find it in the manual and then once I figured out what the manual said.. was so easy.
1. In the Test Plan, switch to the grid view.
2. Filter out the tests in which you want to change the responsible tester.
3. With only the tests that you want to update showing in the grid view, from the main menu click Edit-> Replace. You can choose which field you want to update and put in an appropriate entry.
4. Click Find Next then Replace. Or Replace All.
The Replace All is a scary procedure 'till you are confident of what you are doing.
You have to be in the Grid View to be able to use Replace
Changing it in Test Plan will not put the values in Test Lab (where a Test Set resides as the original poster asked).
The concept will still work, but you need to
1) be in the Test Lab module
2) have the individual Test Set highlighted
3) ensure the Responsible Tester column is shown on your screen
With all of those items in place, the concept will still work as explained. Test Lab/Test Sets are by default in a grid display, so there is no need to switch the views - doing so will only change the way the folder structure is shown and not the individual test sets.
Insanity: doing the same thing over and over again and expecting different results