The default religion name is merely a suggestion, it has no effect on gameplay whatsoever. You can change it if you want. The idea is that you create *your* religion and pick beliefs that fit your strategy.
For example: Suppose you play a civilization with cool medieval units (such as Songhai) and aim for domination victory. Let's say your capital is located in the flood plains with quite a few desert tiles nearby.
So, you decide to pick Holy Warriors as your first follower belief. You realize that you are going to need lot of extra faith to build a sizable army. Thus you pick Desert Folklore pantheon (might as well take advantage of your location) and plan to build Petra ASAP. Of all the buildings that can be purchased with faith, Mosque (+3 faith) is the fastest to pay for itself so might as well pick it as your second follower belief.
Now, you realize that you will need some extra happiness otherwise your warriors will loose their zeal (seriously, negative happiness is *very* bad) after only a few conquered cities. Might as well pick Ceremonial Burial as your founder belief.
Finally, as you will buy as few missionaries as possible, it would make sense to pick something that helps your religion spread on it's own such as Religious Texts.