This should be relatively easy to clear up. In my experience there are a significant number of companies (legal entities) that are called "Something Boring Ltd" but they choose to trade as "Something Really Intersting". A quick look at the Approval Certificate (which should be hanging on the wall in the FTO) will answer the question with the CAA not being averse to issuing an approval saying "Something Boring Ltd trading as Something Really Interesting"
Any monetary transactions may have Something Really Intersting written across the top of an invoice (normally with a snazzy logo) but the Someting Boring Ltd name needs to be visible in the company details bit (including registration numbers etc) written in a very small font across the bottom.