Since the Paris bombing there has been a new push to call the Islamic State "Daesh". Personally, I don't think the name matters. I tend to use both "the Islamic State" and "ISIS" alternatively on this site. I like ISIS because it lets me do stupid jokes about a tv show that I watched when I was a kid. I switch ISIS out with "Islamic State" periodically just to avoid overusing ISIS.
I don't think there is any moral superiority with using "Daesh" as some people have recently argued. The argument for "Daesh" is that the other three names: "the Islamic State", "ISIS" and "ISIL" all include "Islamic" (that is what the first letter in both ISIS and ISIL stands for) which implies that the group is really Muslim when many mainstream Muslims claim that the group is really a perversion of the faith.
That argument is really dumb. Because "Islamic" is in "Daesh" just as much as it is in "ISIS" or "ISIL." "Daesh" is simply the transliteration of "داعش", which is the acronym in Arabic for the group's Arabic name, "الدولة الإسلامية في العراق والشام" (ad-dowla, al-islamiyya fii al-iraq wa-ash-sham). Al-islamiyya ( الإسلامية) or "Islamic" is part of the groups name in Arabic and the ا in "داعش" ("Daesh") stands for the Arabic word for "Islamic" just as the initial "I" in "ISIS" and "ISIL" stands for "Islamic" in the acronym for the English translation of the name,
Maybe there are good reasons to think that "Daesh" is a better name for the group than the alternatives. But those reasons should not be because "Daesh" takes "Islamic" out of the name. It just doesn't.