This is a bizarre use of triggers, but if you really want this to happen, maybe calling a function from the trigger would work.
Alternatively, why not try an INSTEAD OF trigger and replace the UserName with SQL_TEST only if it equals test_user? I'm guessing that's what you're trying to achieve?
For example:
CREATE TRIGGER users.insert_log
BEFORE INSERT ON users.logBook
FOR EACH ROW
BEGIN
IF NEW.UserName = 'test_user' THEN
SET NEW.UserName = 'SQL_TEST';
END IF;
END;