So first off, I loved Teen Titans (2003). I can openly admit that I am very biased to it, and incorporate it into my personal complicated au. In Teen Titans, Dick leads them as Robin. So lets talk about Jason, and how Dick becomes Nightwing. (In my au)
"Red X is Jason Todd!!" No. Red X is clearly Grant Wilson. It makes the most sense. He calls Robin "kid" implying that he is older, has a similar fighting style to Slade (because we know he and Robin are similar), and most importantly, Jason would not die and come back to find Dick in the Robin costume. (Unless it's a reverse au).
So since Robin leads the Teen Titans, still Robin despite not being in Gotham or with Batman, why would he become Nightwing? Here is my answer.
Dick finds a newspaper article about Batman and Robin in Gotham. Recently. He hasn't been in Gotham recently. There are speculations on why there are two Robins.
He goes home to confront Bruce, and finds a child that looks just like him, in a previous version of his costume. He argues with Bruce, he visits Clark, hears the story about Nightwing and Flamebird, remembers that one episode where Starfire went to the future, and returns to Jump City as Nightwing, unable to take Robin away from the kid, officially giving up Robin to Jason.
Jason doesn't any of know that and believes he has always lead the Titans as Nightwing.
(The newspaper is also a parallel to how Dick found out about Jason's death :D)
Do with this what you will.