A business with a "fictitious business name" is a real, live business. "Fictitious" refers to naming a business something other than the registered business name:
From
Register Your Fictitious or "Doing Business As" (DBA) Name | SBA.gov :
"
A fictitious name (or assumed name, trade name or DBA name) is a business name that is different from your personal name, the names of your partners or the officially registered name of your LLC or corporation."
Bill