The story
An acronym of one English translation of one of the group's Arabic-language names, الدَّوْلَة الْإِسْلَامِيَّة فِي الْعِرَاق وَالشَّام (ad-dawla l-ʔislāmiyya fī l-ʕirāq wa-š-šām, literally “the Islamic State in Iraq and the Levant”). Compare ISIS, which translates الشَّام (aš-šām) as “Syria” rather than “the Levant”.
Etymology from Wiktionary, CC BY-SA 4.0.