Actually, the “L” better indicates the greater ambitions of IS.
They are not just about Iraq and Syria, they want the whole Middle East ... most especially Israel.
Recognizing that can actually be actually a good thing.
At the very least, ISIL is code for “I’m a smart person” because you’ll notice that elitists generally use it rather than ISIS. Another example is our Canadian prime minister. I am not convinced that anyone using ISIL instead of ISIS has an overt anti-Israel agenda, some may use the alternate name just to appear smart. Obama of course has already proven he is no friend of Israel, so this is not a point that needs to be tested again.
In some ways it might be better politically to recognize the existence of their state then declare war on it. This would get around the problems of military exercises on territory that is nominally Syrian. Recognizing the existence of a state does not imply accepting its policies or even setting up any form of contact. We certainly recognized that the Taliban was running Afghanistan in 2000 and dealt with that accordingly.