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The choice of the word Daesh is a western acronym for 'al-dowla al-islaamiyya fii-il-i’raaq wa-ash-shaam' = 'Islamic State in Iraq and Syria'.
Daesh is five letters not four (‘in’ and ‘and’ are omitted so it's just ISIS/L) because the Arabic letter 'ع' which begins the word for 'Iraq' is difficult/impossible to pronounce for an anglophone hence the use of an 'e' (or occasionally an ’e) in the transliteration.
They don't really use acronyms in arabic so they consider it to be a funny made up word not the legitimate 'Islamic state' title they want. I think that a lot of people are reluctant to legitimise their status by calling them the Islamic State/ISIL/IRAQ too, and I know some (I think the French and the US) have been particularly keen on only using the term daesh and avoid any official sounding titles etc.
Why the preference for referring to them as Daesh?