According to multiple sources DAISH, is simply a transliteration of the Arabic term that these terrorists' call themselves: al-Dawla al-Islamiya al-Iraq al-Sham (Islamic State of Iraq and the Levant), i. e., ISIL. It seems to me that either iteration advances the fiction that either they are of, or are representative of, the Ummah.
Although the Anglo world prefers the Angloized iteration (and aren't we all former British subjects writing in English, here) and does not defer to the language used to identify them by some of those who have suffered by their atrocities, as many in the non-Anglophone world do, my independent interpretation of the two iteratiions is that the only technical difference between the two is the language, a linguistic orientation or choice.
Kurdish and Yadzidi communities have also suffered greatly by these terrorists' hand. And, as Kurdish units have had the greater and more significant successes against them in battle, thus far, is their linguistic name for ISIL not equally as valid as the Arabic? And,what of Yadzidi peoples; is their linguistic name for ISIL not equally as valid as the Arabic? Is it actually political correctness to prefer one to the others, or is it simply the privileging of one over the others? In that sense ISIS/ISIL is to DAESH/DAISH as DAESH/DAISH is to Kurdish and Yadziki iterations.
Cultural relativity and the cultural sesitivities it fosters are very useful analytical positons and interpretive considerations; nevertheless, when attempting these considerations, it is vital that one recognize all of the cultural stakeholders within a given context. Consequently, it is simplistic and reductionist to suggest that only Arab peoples have suffered these terrorists' atrocities and therefore, their name for the group is the correct one. As I've stated here once before, as to matters of which I am only an observer, I prefer to use infinitive as opposed to definitive terms. This creates an environment for discourse that actually welcomes alternative interpretations and diminishes the potential for conflict.
The world has never spoken one language, and hopefully, never will.