Taiwanese can register DBA / ‘trading as’ organisations but as far as I know foreigners are restricted to various types of limited companies. You would also not be able to do anything in Taiwan like set up a branch/representative office with a foreign company not limited by guarantee (ltd.)
Setting up legally in Taiwan is quite possible but can get complicated. Rather than waste your money on a CPA who will charge you big bucks to fill out a couple of forms I would suggest speaking to your local MOEA office (either in Taiwan or abroad - the foreign MOEA branches can be particularly helpful). As long as you present yourself as someone worth the effort they will sit down with you and go through all the options available, plus a list of things you need to provide for registration in Taiwan.