The business is incorporated.
The laws of business filings with respect to incorporation, names, etc. will vary from state to state. The best definitive resource (other than a lawyer) is your Secretary of State web site for your state of incorporation. In my experience, I have filed a registered name which created a DBA (doing business as) name. I was able to advertise and operate on this name with the need use DBA for certain legal documents, such as checks. On invoices, it would put my DBA name and underneath put (a Division of ParentCo, Inc.).
