Possibly, the last letter is a U, not a V. (With the lettering design following the patch edge, you couldn't round off the bottom of a U.) It might have been an archaic representation of NorthCarolina NAtionalGUard.
Military Assistance Command - Vietnam MACV was created on February 8, 1962, in response to the increase in U.S. military assistance to South Vietnam. MACV was therefore disbanded on March 29, 1973.
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North Carolina Nuns Against Gun Violence
NC Naval Advisory Group Vietnam
NC Neighbors Against Gang Violence
Nuckolls County Nebraskans Against Gun Violence
North Carolina Northeast Academy Girls Volleyball It looks like a lettermens jacket patch; being made of felt.