You cannot change a table while the INSERT trigger is firing. The INSERT might do some locking which could result in a deadlock. Also, updating the table from a trigger would then cause the same trigger to fire again in an infinite recursive loop. Both of these reasons are why MySQL prevents you from doing this.
However, depending on what you're trying to achieve, you can access the new values by using NEW.fieldname or even the old values--if doing an UPDATE--with OLD.
If you had a row named
full_brand_name and you wanted to use the first two letters as a short name in the field
small_name you could use:
CREATE TRIGGER `capital` BEFORE INSERT ON `brandnames`
FOR EACH ROW BEGIN
SET NEW.short_name = CONCAT(UCASE(LEFT(NEW.full_name,1)) , LCASE(SUBSTRING(NEW.full_name,2)))