The decision was taken "a few days ago" by the chiefs of all the armed services, said Colonel Ed Thomas, spokesman for the US military's top officer, General Martin Dempsey.
"The operation is called 'Operation Inherent Resolve,'" Thomas told reporters.
The spokesman offered no explanation as to why the Pentagon chose that name, which had already been cited in media reports as a possible choice that was rejected by some officers.
The US military usually announces the name of a military operation from the start.
During the subsequent US occupation of Iraq from 2003 to 2011, there were more than 500 named operations, including Operation Airborne Dragon and Operation Tapeworm.
But since warplanes started bombing the IS group in Iraq in early August, the mission has had no official moniker, prompting a spate of speculation and sarcasm.
Some commentators alleged the White House was hesitant to give the operation a name due to a lack of enthusiasm for intervening in Iraq and Syria. But US officials dismissed the idea as ridiculous.
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