Seems like this has been long running legal dispute, but as of right now GC has ownership of the name in the US. Smart move by General Cigar to register the name in 1978....
"
In response to General Cigar's use of the Cohiba name, Cubatabaco, the government-run company in charge of cigars, and half-owner of Habanos SA along with
Altadis SA, launched a long-running legal campaign to have General Cigar's trademark revoked.
These legal fisticuffs were resolved on June 19, 2006, when the
U. S. Supreme Court denied Cubatabaco's petition. As a result, the February 2005 decision of the
U. S. 2nd Circuit Court of Appeals (Docket #04-2527), which confirmed General Cigar Company’s exclusive ownership of the Cohiba trademark in the United States, is final.
[10] The General Cigar-made Cohiba cigars now have a disclaimer on boxes that they are not affiliated in any way with the Cuban brand.
However, the United States government, in an
amicus curiae brief filed in the Supreme Court, acknowledged that Cubatabaco could request U.S. government permission for judicial protection of the brand from the
Department of the Treasury's
Office of Foreign Assets Control, which administers the U.S. embargo. Cubatabaco has stated that they intend to pursue this course of action."