Query columns will use the underlying field name as the header on the results page. To change the name of a column in your query results, first navigate to the query design screen. Select the field you would like to rename, and in the properties pane on the right of the screen, click the field name to edit the description.
As you change the field description, you will see the original field name appear above for your reference:
Once you've renamed the appropriate fields, run your query and you'll see that the columns are now labeled with the new field name descriptions. This trick can be particularly useful when creating data package exports that must have specific column names.