Before you register a DBA name (i.e. Doing Business As, also known as Fictitious Business Name), you need to make sure that a given name is available. For a San Francisco business, you can do an on-line search of existing names here. If the name you chose is not on that list, you’re good to go.
As a side-note: registering DBA in California requires posting a notice in the newspaper. First, it’s oddly antiquated in a state that is home to Silicon Valley. Second, what will happen after the inevitable downfall of paper editions of newspapers?