In April 2013, having expanded into Syria, the group adopted the name ad-Dawlah al-Islāmiyah fī 'l-ʿIrāq wa-sh-Shām (الدولة الإسلامية في العراق والشام). As
al-Shām is a region often compared with the
Greater Syria, the group's name has been variously translated as "Islamic State of Iraq and
 "Islamic State of Iraq and Syria"
 (both abbreviated as ISIS), or "Islamic State of Iraq and the Levant" (abbreviated as ISIL).
While the use of either one or the other
acronym has been the subject of debate,
 the distinction between the two and its relevance has been considered not so great.
 Of greater relevance is the name Daesh, which is an acronym of ISIL's
Arabic name al-Dawlah al-Islamīyah fī al-ʻIrāq wa-al-Shām. Daesh, or Da'ish (داعش). This name has been widely used by ISIL's Arabic-speaking detractors,
 although – and to a certain extent because – it is considered derogatory, as it resembles the Arabic words Daes (lit. "one who crushes, or tramples down, something underfoot") and Dāhis (loosely translated: "one who sows discord").
 Within areas under its control, ISIL considers use of the name Daesh punishable by flogging
 or cutting out the tongue.
In late June 2014, the group renamed itself ad-Dawlah al-Islāmiyah (lit. Islamic State or IS), declaring itself a worldwide
 The name "Islamic State" and the group's claim to be a caliphate have been widely rejected, with the UN, various governments, and mainstream Muslim groups refusing to use the new name.
 The group's declaration of a new caliphate in June 2014 and its adoption of the name "Islamic State" have been criticised and ridiculed by Muslim scholars and rival Islamists both inside and outside the territory it controls.
In a speech in September 2014, President Obama said that ISIL is not "Islamic" on the basis that no religion condones the killing of innocents and that no government
recognises the group as a state,
 while many object to using the name "Islamic State" owing to the far-reaching religious and political claims to authority which that name implies. The
United Nations Security Council,
 the United States,
 the United Kingdom
 and other countries generally call the group "ISIL", while much of the Arab world uses the
Arabic acronym "Dāʻish". France's Foreign Minister Laurent Fabius said "This is a terrorist group and not a state. I do not recommend using the term Islamic State because it blurs the lines between Islam, Muslims, and Islamists. The Arabs call it 'Daesh' and I will be calling them the 'Daesh cutthroats.'"
 Retired general
John Allen, the US envoy appointed to co-ordinate the coalition;
U.S. Army Lieutenant General
James Terry, head of operations against the group; and
Secretary of State
John Kerry had all shifted towards use of the term DAESH by December 2014.