it's not possible because there is no NEW or OLD table. The entire trigger is related to the table - the "new" and "old" refer to the rows and the values they contained before and after the event that was triggered. In other words, your example would be:
call logChanges(OLD.customername, NEW.customername)
You could also save all the OLD data in a history table (which I expect logchanges does anyways), basically being a clone of the production table something like this:
BEGIN
IF OLD.customer_name != NEW.customer_name
THEN
INSERT INTO myTable_chagne_history
(
customer_id ,
customer_name ,
another_field ,
edit_time
)
VALUES
(
OLD.customer_id,
OLD.customer_name,
OLD.another_field ,
NEW.time_edit_was_made
);
END IF;
END;