Doing Business As Name Registration for Nonprofit

A nonprofit organization is currently registered to solicit for donations in many states and is looking to solicit in every state. The organization is incorporated in the state of new York but is located in Tennessee. If the organization is soliciting under a different name, where do we need to register the new name. NY and TN or every state? Can we even register a trade name without having a business license in a state? Also, if the organization adds applies for more business licenses do we need to register the DBA in those states too?