In ancient Mesopotamia, authors didn't get too creative with the titles of their works. Remember, this is the oldest literary work we have—so the Sumerians may have just referred to it as "that one piece of literature we've got." Later, though, the usual way to name a book was by using its opening words.
The opening words of Tablet 1 are (in the Kovacs' translation) "He Who Has Seen Everything." That sounds like a winner to us, but when the poem was rediscovered by the Englishman George Smith in the 1870s, people just started referring to the work by the name of its hero, Gilgamesh—maybe paralleling the way the poem Beowulf is referred to by the name of its hero, Beowulf. Today, you'll sometimes find copies of the work known simply as Gilgamesh (the popular Stephen Mitchell version follows this tradition).
But other translators decided to get fancy, sticking a classification on the beginning of the name for good measure. As a result, the poem became known as The Epic of Gilgamesh—as it is in most translations, including the version by Maureen Gallery Kovacs that we're using on Shmoop.
Sure, it's a long poem dealing with adventures and heroes and stuff, but we think the term "epic" is a wee bit misleading. That's because the word "epic" comes from the Greek tradition of Homer and Hesiod, and the Ancient Babylonians might not have thought about this work in the same way the Greeks did about the Iliad and the Odyssey.
So, you can't blame us at Shmoop if we have a bit of a soft spot for plain old Gilgamesh. We would also be in full support of your campaign to bring back the classic "He Who Has Seen Everything." Call us. We'll do lunch.