Brands are not legal entities, they are just brands. Even if you chose to trademark your brands, and your existing company would own those trademarks.
There is nothing wrong with have more than one brand under a single company name, this happens all the time especially in the product space (Nabisco or any other major food manufacturer has tons of brands under the parent company).
Now I don't know where you live, but the only issue I am aware of is in relation to operating without registering a business name. In Canada you can operate a business without registering your business name if it is your name followed by what you do. In my case Douglas Portz Photography. That does not need to be registered as a name. If I wanted to operate as some other name, then I need to register the name.
registering a name does not require an incorporation, it can be a partnership or sole owner.
If the plan is to still use the same bank account and have clients pay a single entity, you may be okay to use a different name from a brand perspective only. I say may as I don't know the laws outside of my Province within Canada, so a quick call to your local business licensing office or economic development office could answer those questions.
In my case I have the name of my company, but I have 2 different brands, one for my corporate work, and one for my sports work. regardless who my client is, the bills are the same, with my company name on the letterhead, and on the invoices, all the money goes into the same account.