Yes, in most cases you can run two brands from the same white label setup, although how separate they can really look depends on your plan and on which parts you need to differ.
The usual arrangement is one account behind the scenes with two front ends. Each brand can have its own web address, its own logo, colours and homepage, and its own contact details on the pages and the confirmation documents, so a corporate client and a walk in customer would have no reason to think they are looking at the same business. On many setups you can also set different markups for each brand and decide that one of them asks visitors to log in before they see any fares, which is what most agencies want for their corporate side. Your bookings from both brands still land in one place for you, which is normally an advantage because you are not logging in twice to see your day's business.
What is shared is worth checking carefully. Supplier connections, and the credentials behind them, are generally held once at the account level rather than per brand, so both front ends draw on the same inventory. Some wording, such as standard terms or cancellation text, may also be set once unless your plan allows it per brand. If you need the two brands to behave quite differently, for example different suppliers altogether or different payment providers, that can sometimes mean a second portal rather than a second skin, and that depends on what you are signed up for.
Before you commit, write down a short list of what genuinely has to be different between the two brands and what you are happy to share, then send it over so we can confirm which of it your plan covers.