IS/Islamic State/ISIS/ISIL?

We've been hearing about them almost incessantly for the better part of the year. They'd seemingly started calling themselves the Arabic equivalent of ISIS, and then later "decided" to call themselves instead Islamic State, reasons in the news being they're exerting independence and individuality apart from Syria, the Levant, and Iraq.

Some media outfits, like Deutsche Welle, Al Jazeera, and elements of the BBC, had followed suit and called them IS or "the Islamic State group", still acknowledging some still call them ISIS or ISIL. I've never quite understood concretely why some elect to call them one way or another.

American news outlets like CNN and Fox News still predominately call them ISIS, and I think it may be partly because the US government in general still calls them that as well.

Is it perhaps to deny them the "satisfaction" of hearing people address them with the name they wish people to call them? I wouldn't doubt that's a probability, but there hasn't seemed to be any discussion on that. It's also seemed there are some who had gotten so used to calling them ISIS, or ISIL, that they just continue calling them that since all of it is generally coterminous.

It reminds me of something else I'd brought up in the past about maps that showed Crimea as still part of Ukraine rather than, at the least, showing it as a disputed area that happened to have had a referendum deciding to cede themselves to Russia.

I believe they should do both, at the very least, much like Deutsche Welle has done ("the Islamic State, also called ISIS"). That seems to be the fairest thing in my view.