If you want to use a drag selection to quickly select many nearby designators: Use the Selection Filter to turn on only Texts. Then hold the Ctrl key down while clicking and dragging the cursor to select all the designators within the selection box. *** Be careful. Your selection may include other unwanted text objects. If so, you can hold down the Shift key to click on individual text objects to toggle their selection status. ***
You can get to the Selection filter from the Active Bar
The defined filtering in the Active Bar's pop-up pane will be reflected in the Properties panel. Conversely, changes made to the filter in the Properties panel will be instantly reflected back in the pop-up pane from the Active Bar.