As of 15 October 2014, the U.S. military operation name Operation Inherent Resolve officially refers to the US's military actions against ISIL, specifically the campaign in Iraq and the campaign in Syria.

Operation Inherent Resolve (OIR) is the U.S. military's operational name for the military intervention against the Islamic State of Iraq and the Levant (ISIL, in the vernacular, Daesh), including both the campaign in Iraq and the campaign in Syria.
Unlike their coalition partners, and unlike previous combat operations, no name was initially given to the conflict against ISIS by the U.S. government. The decision to keep the conflict nameless drew considerable media criticism.
The U.S. decided in October 2014 to name its military efforts against ISIS as "Operation Inherent Resolve"; the U.S. Central Command (CENTCOM) news release announcing the name noted that:

    According to CENTCOM officials, the name INHERENT RESOLVE is intended to reflect the unwavering resolve and deep commitment of the U.S. and partner nations in the region and around the globe to eliminate the terrorist group ISIL and the threat they pose to Iraq, the region and the wider international community. It also symbolizes the willingness and dedication of coalition members to work closely with our friends in the region and apply all available dimensions of national power necessary—diplomatic, informational, military, economic—to degrade and ultimately destroy ISIL.

The Defense Department announced at the end of October 2014 that troops operating in support of Operation Inherent Resolve after 15 June were eligible for the Global War on Terrorism Expeditionary Medal. Service areas are: Bahrain, Cyprus, Egypt, Iran, Iraq, Israel, Jordan, Kuwait, Lebanon, Qatar, Saudi Arabia, Syria, Turkey, and the United Arab Emirates, as well as troops supporting the operation in the Persian Gulf, the Red Sea and the Mediterranean Sea east of 25 degrees longitude. The medal is approved retroactively beginning 15 June, the Pentagon said.