The New United Nations Government post-SDF Macross: While the "New United Nations Government" was spoken when referring to the Earth government immediately after Space War I and for the remainder of the SDF Macross series, the sequels Macross Plus (1994) and Macross 7 (1995) instead revert back to the phrase "United Nations Government" or "United Nations Spacy".
NUNS acronym in Macross II: In 1992 the OVA sequel Macross II was produced and utilized the title "NUNS" in several sequences throughout the series. However, the acronym "NUNS" does not refer to the government or military (This is Animation Special #5 clearly refers to the military of the Macross II world as the UN Spacy and the acronym UNS can clearly be seen on military uniforms in the anime). The acronym "NUNS" is a news station in the Macross II world (the NUNS logos can be seen on microphones used by news agents) however the full name for the acronym is never revealed.
The New United Nations Government in Macross Frontier: In 2007 the sequel Macross Frontier was produced and began utilizing the "New United Nations Government" title for an administration that ruled human civilization not from Earth, but from aboard the mobile colony fleet Macross Frontier. However, in this sequel, the private military contractor Strategic Military Services (SMS) has come to play a very prominent role in the defense and military policy of this new government.
Creator Shoji Kawamori has stated (interview from Otona Anime magazine #9) the New U.N. is a newly organized and decentralized government of the human colony fleets and colony worlds. Kawamori states that Earth is no longer able to directly control the hundreds of colony world and fleets given the vast interstellar distances involved. This change in government was not a coup or revolution, but a realigning of the galaxy at large. Thus U.N. colonies and fleets became self-governing but belong to the New United Nations as members.