National Office of New Americans Act This bill establishes the National Office of New Americans (NONA) within the Executive Office of the President to promote and support the integration of immigrants and refugees into the social, cultural, economic, and civic life of the United States. The NONA shall also establish the Federal Initiative on New Americans. The initiative shall establish a coordinated federal program to respond effectively to immigrant and refugee integration issues such as language learning, adult education and workforce training, health care, and naturalization.