Doing Business As: denotes a business name used by a person or entity that is different from the person's or entity's true name. DBAs are not separate entities and do not shield the person or entity who uses the DBA as a business name from liability for debts or lawsuits. Filing requirements vary and are not permitted for some types of businesses or professional practices. See also Delaware corporation, Delaware statutory trust, Nevada corporation, and Massachusetts business trust.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.