Do you plan to use a pen name aka pseudonym aka nom de plume?
If your pen name will be an open secret and your main purpose in using one is to differentiate between the various genres you write in, go ahead and register a DBA (fictitious business name) for your pseudonym. Having a DBA will allow you to set up bank accounts and rent mail boxes in the name of the pseudonym. You can register a DBA with your local government, usually the county clerk. (This information applies to writers in the U.S.)
If you want your legal name to remain a secret, do NOT register a DBA! In California, after registering the DBA you then have to publish a notice in a general-circulation newspaper for four consecutive weeks. Your name and street address are published in the notice. You can’t use a P.O. box for your address.
When you publish through Kindle Direct Publishing and similar online vendors (verify for the vendors you work with), they don’t care what author name is assigned to a particular book. Payments will go to the main account name, eliminating one of the primary reasons to have a DBA: so you can receive checks in that name.