If your nonprofit has one "corporate" name but uses another name, the second name is known as the D.B.A., or "Doing business as." For instance the corporate name may be "Nonprofit Services for the Elderly," but you might use the name, "Guardian Angels" on stationary, signage, logo, etc. The nonprofit must register the D.B.A. name with the state in which it is doing business.
An organization might have several D.B.A.s. One could be its primary name and others could be the names of specific programs. All names should be registered and undergo the same level of legal checking as your corporate name. For more details on trademarking issues, see How to Find a Name for Your New Nonprofit - Making It Legal.
Nonprofit Services for the Elderly is better known as Guardian Angels.