"Medieval Islamic Civilization"
So why do I call my undergraduate course "Medieval Islamic Civilization?" One reason is that I think the point about Islam's geographic diversity is worth communicating to undergraduates, and that just mentioning it at some point when discussing the basics of Islam doesn't do the trick. You actually have to introduce them to the introduction of Islam in Africa, South Asia, Southeast Asia, and other places, and see them as important components of the "Islamic world." This is especially tempting at a small liberal arts college that doesn't have courses in all of these regions, and where this course might be the only exposure to their history for which many students will have the opportunity.
Another is that I think it can be used to make a subtle point about the way we label the world, and how our geographic regions are often modern constructs with little relevance to people in the Middle Ages. I once considered doing a dissertation topic that would have involved Yemen, Ethiopia and Somalia, and was struck by the bureaucratic obstacles certain funding agencies had to projects which involved more than one "geographic region." I rather doubt that medieval travellers had a sense that crossing the eastern border of modern Iran thought of themselves as leaving the "Middle East" for "South Asia."
In practice, this labelling doesn't change much of the content, as most regions outside the Middle East won't come up until late in the course, and I still deal with Middle Eastern Christianity and Judaism in almost the exact same way I would otherwise. One does have to be careful about the implicit labelling of, say, a discussion of medieval Arab housing as "Islamic," but I'm willing to deal with that when the time comes. I don't know if I'll do it this way throughout my career, but it feels the right decision for my current situation.