The term al-Sham (Sham, for short) in Arabic means the land of the left hand because it was to the north of Arabia. This refers to the person facing the rising sun in Arabia, thus leaving north on the left hand side. Sham has long been used in classical Arab and Islamic geography to mean Syria, however, not the land of the modern Syrian Arab Republic (سورية , Syria) but the historic region of greater Syria. For example, the Roman Syria included modern-day Syria, Lebanon, and parts of Turkey while Ottoman Syria also included Israel, Jordan, and parts of Saudi Arabia and Egypt. Basically, the historic region of Syria is a near perfect match for the western concept of the Levant.
So, a close to literal translation has the group being "Islamic State of Iraq and Syria", however, most readers are likely to confuse greater Syria (al-Sham) with the modern state of Syria. Because al-Sham is a near perfect fit for the concept of "Levant" and they have made clear their goals are more Leavant-oriented I recommend using the term the Islamic State of Iraq and the Levant.
|The ISIL is not a fan of the small boundaries of the Syrian Arab Republic and prefer al-Sham instead. Photo via Twitter.|