Appropriated Title

Appropriated Title is when a franchise is better known by a different title than it was originally known as. There can be various reasons for this:

The sequel was more successful, or at least more famous.
The original title would be an Artifact Title if the series continued to use it.
The sequel's name just sounded cooler.

Examples of Appropriated Title include:

The first Rambo movie was actually called First Blood. It wasn't until the sequel, Rambo: First Blood Part II, that the Rambo name was used at all, followed by Rambo III. This enabled them to call the fourth film Rambo, since that name was never actually used.
The first release in the Chronicles of Riddick canon was called Pitch Black. This goes along with the complete change in tone and focus the series underwent after the first installment.
The first Indiana Jones movie was just called Raiders of the Lost Ark, while all other media include Jones' name in the title. For what it's worth, later re-releases did change the title to Indiana Jones and the Raiders of the Lost Ark.
Early games starring Mario went under a variety of titles, the most well-known games being Donkey Kong, Mario Bros., and Wrecking Crew. It wasn't until Super Mario Bros, the 15th unique game in the series (counting Game & Watch spin-offs), that the series finally got a definitive title.
The ninth, tenth, and eleventh Friday the 13th movies went under the Jason name. However, this was only out of necessity, as New Line did not own the rights to the Friday the 13th title; once they bought them, the series reverted to its original name.
In an unusual case of entire companies doing this, DC Comics, Archie Comics, and Marvel Comics all got their names from their previous incarnation's most popular title.
Although Alien's third and fourth films went under the original title, most spin-off merchandise is known under Aliens, which was the second movie.
Batman Begins has two sequels, both under the Dark Knight name, in what has come be known as The Dark Knight Saga.
If you can believe it, the Star Wars series was originally meant to be called The Adventures of Luke Skywalker. The first film's tremendous success and fame negated this.
Super Mario Land 3: Wario Land and Super Mario World 2: Yoshi's Island both had sequels that went by their subtitles' names. Though, the originals weren't really sequels anyway.
The adaptations of Scott Pilgrim take their name from Scott Pilgrim vs. The World, the second book in the series.
The X-COM series started as UFO: Enemy Unknown. It had to relabel itself X-COM when somebody complained there's already a game called UFO. And a television show.
The Soul Series was originally called Soul Blade but is now better known as Soul Calibur.
Men Who Hate Women, from The Millennium Trilogy, is most often better known as The Girl With The Dragon Tattoo, its English title. The sequels in English are The Girl Who Played With Fire and The Girl Who Kicked the Hornet's Nest.
The Dark Forces title was replaced with Jedi Knight when the second game (Dark Forces II: Jedi Knight) proved more popular.
Thomas Harris's series of books featuring Hannibal Lecter began with Red Dragon, but it's known as the Silence of the Lambs series due to the popularity of that film.
The Dark Is Rising takes its series title from the second book in the sequence.
Gormenghast is given a series title taken from its second book (and from the setting of the first two books). However, this was contrary to the designs of the author, who had intended that the series would centre around the doings of the title character of first book, Titus Groan, who leaves Gormenghast Castle to journey the outside world at the end of the second book.
In the states, the Ace Attorney series began with the game Phoenix Wright Ace Attorney, with the intention of the series being called Phoenix Wright. The announcement that the fourth game would star a new character prompted the American publishers to release all future releases under the Ace Attorney title, leaving the first game the odd one out.