1) As already stated, the game was not built to allow for such a thing. Making it available is probably no small feat at best, and may require a massive effort.
2) Without easy access to global handles, it could allow for a massive amount of trolling and in-game fraud. This is another thing that would have to be changed, not just letting people use the same names as other players.
3) It goes against the source material.
Yeah, I know that this isn't the best argument against it, but I rather enjoy the fact that every character is the one and only.
Also, I am aware that there have been occasions where two characters have simultaneously had the same name, but it was usually a source of contention and one of the characters stopped using the name.
There are plenty of examples of names being abandoned and adopted by someone else.
I sincerely hope that you didn't just see someone else's character and think "cool name. I want it", because the lack of imagination involved in that hurts to think about.
But if you have a name, however imaginative you may have thought that it was, but someone else has it, there are ways around that.
Add letters. Add numbers. Change letters. Add colors or other adjectives.
So I really wanted to make a character called Titan. Basic, but that's what I wanted. Unfortunately, it's taken or otherwise unavailable.
Okay, I have options.
Titan 1
T1tan
Red Titan
Titan Red
Tytan
Titanic
Tytanic
Titanik
Tytanik
Ti-Tan
Ultra-Titan
Dr. Titan
Everything still contains that base Titan, but allows not only whoever has Titan (assuming it's not banned for use for whatever reason) to keep it unique to themselves allowing them to build a reputation of their own, but it also allows you to have an identity and reputation of your own, too.