smallbusiness.co.uk: Helping your business think big

This is a difficult question to answer without knowing more detail, but I would suggest the main consideration, based purely on the information in the question, is one of cross selling.

This means getting your exercise class customers to buy your clothes, and your clothes customers to sign up for classes. Of course, your market for clothes is much, much bigger as it is not as limited by geography the other part of the business.

Selling over the internet is an opportunity for you. There is nothing stoping you using the existing company to branch out, but if the current company name is obviously related to exercise classes, you might want to consider changing it to something more generic.

If not, why not keep it the same, especially as your name is already known in the classes market and will thus help initial clothes sales?