For some characters, it’s really the powers, or the name, that define the character–Green Lantern, Flash, Captain Marvel (both the DC and Marvel versions), Thor, Robin, Iron Man.
For others, it’s the person–Superman isn’t Superman unless he’s Clark Kent. Likewise, Batman, Captain America, Spider-Man, and a few others are so strongly tied to a specific version of the character that it’s just not the same character if you substitute some radically different version. With characters like these, if you want to have a radically different version, you have to keep the original around and add the others as a spinoff. Thus, it’s ok to have a female version of Spider-Man (Spider-Girl, all three Spider-Woman characters), because she didn’t replace him, but was added to the existing continuity.
The debate here seems to be whether Wonder Woman is a title for whoever is the chosen emmisary of the Amazons, or if she has to be Diana. Internally–withing the DC universe–the issue is debatable. Externally, Princess Diana is the one true Wonder Woman.
Let’s go back and revisit Captain America 1985 for a moment. Steve Rogers is asked to work directly for the federal government as their agent or give up the title Captain America, including the costume and shield. He refuses to give up his autonomy, and is stripped of the title and costume, which are given to John Walker, an enhanced super-soldier who used to be the Super Patriot. Steve adopts the title The Captain, and contiues fighting for justice, while the new Captain runs amok, eventually committing cold-blooded murder. Steve eventually returns, takes out Walker, and returns to being Captain America.
This was the plan all along. By replacing Steve with someone who was similar to him in some superficial ways, but who was otherwise much different, it helped bring focus to what it was that made the character who he was. We define characters as much by what they aren’t as we do by what they are.
This has become a standard superhero storyline. Help define what a character is, by showing us what he/she isn’t. Putting someone else in the costume helps to define the character of the person in the costume as distict from the costume itself. But the plan is always to eventually bring back the original, now with a new focus as a result of having been gone. They did this with the death of Superman, with Knightfall, and twice with Wonder Woman (this storyline was, by the way, lifted directly from Pre-Crisis Wonder Woman). Others have worn the title and the costume, but the purpose was always to further define Pricess Diana by showing us a Wonder Woman who lacked some important quality she posessed.
Not post-Crisis. The Amazons were all created by a goddess animating mud with the souls of women who had been murdered by men. Hippolyta was the first woman murdered by a man, and thus was made queen. She was pregnant at the time, and the soul of her unborn daughter later became the life force that animated Diana, so Diana is her true daughter. Amazons, in general, can be of any ethnic group.
However, pre-Crisis and post-Crisis both, Hippolyta is Greek, and thus, so is her daughter. Part of what makes Wonder Woman Wonder Woman is that she’s the Queen’s daughter–it adds drama to have Diana forbidden to enter, then have to disguise herself to win the tournament. But that doesn’t mean that any Amazon can be Wonder Woman. The original tournament and subsequent ones are story devices intended to help define the character. But the character herself was concieved as the daughter of the queen.
It helps to define her character by temporarily having her replaced by someone different. But it always comes back to Princess Diana. She’s tall, beautiful, a young adult physically, muscular yet feminine, and has long black hair, and fair skin.