Just in case you slept through the entire movie, E.T. is one of the main characters, and he's an extra-terrestrial. So E.T. the Extra-Terrestrial isn't exactly the cleverest title in cinema history. It is a little misleading, though, since it seems to suggest that E.T is the main character of the movie. He's not. That honor belongs to E.T.'s BFF, Elliott. In fact, it's Elliott who gives E.T his name. "E.T.," of course, stands for "Extra Terrestrial," but it's also the first and last letters of Elliott's name. That's significant.
It's possible that Elliott's a raging egomaniac with a god complex who wants to mold E.T. in his own image. But it's far more likely that Elliott just wants to have as much in common with his best friend as possible. The interplay between their names hints at the deeper bond that they share.