The group which has been referred to by the acronyms ISIL, ISIS, and IS wants to be perceived as the legitimate Islamic Caliphate. It uses this as a recruiting and fundraising tool. The group is however not regarded this way by the vast majority of Muslims in the world. Using its own terms to refer to it only serves to legitimize its claims.
It would be far better to refer to it as Daesh. This term has a variety of meanings and interpretations. Of the greatest importance though is that it does not reinforce the false claims of the group it is used to describe. The global conflict with this group is not just being fought on the many battlefields of Syria and Iraq. It is being fought in the many various forms of the media and on the world wide web.
The name we use matters.