After reading all of this some thoughts. Tim is one of the few sidekick characters that was given time to grow as a person. His Robin run was a huge thing and defined who his character was. Dick kind of had that, but they did more with Nightwing for him. Jason was going to be a derivative of Dick (he was going to have the same backstory) until they changed it to be distinct as a thief and ran with it after crisis.
Tim started out as someone who just found out the truth due to how Bruce operated with Dick back then, in Daylight hours, and Tim took his picture. He figured things out. And even though Dick opposed the idea, eventually he became Robin. All the neat tech stuff came from Dixons run.
Tim also had, like Dick the most solid civilian stories, and the most normal life until writers were like kill his family off for drama. Second closest is Steph and Babs. DC originally had no plans on moving him up (Hell they originally wanted Dick to keep the Robin name in Teen Titans and Marv said nope, new name needed) since he was going to be THE Robin as why would you replace the fan favorite.
Then Grant came in and They wanted to write a story about how divorce can affect a kid. Thus they used Damian, and he was supposed to remain dead. DC liked him and if not for Tomasi and I would argue Snyder and a few other writers like BQM, in no way would Damian be as popular as he is now.
DC really wanted to push the true son narrative and new fresh teens, so they fucked up the generation before,Tim's group. That's why we're in this spot with them.
Tim also wouldn't be the first Robin to hold that title for so long. Earth 2 Dick Grayson kept it while he worked with Helena Wayne, Bruce's daughter.
As for the latest writer, I am really not enjoying how she is doing this arc for YJ, out right making it seem like Batman would be against Tim dating a guy. And again fucking over Steph. Even if this is a Twist, where she wants you to go, this isn't right,this was not the group to tackle this with regarding the team. Also character assaination of Arrowette. And I feel like she could have picked a way better love interest for Tim.
As for names, Redbird is a moniker that Damian took. Flamethrower is Betty Kanes. Redwing and Darkwing are both owned by Marvel and Disney. And, because DC has a thing for birds (Talon, Starling, Bluejay), it limits what writers can pick.
I still think Red Robin is the best choice going forward for him. Its a name that already existed via Kingdom Come, and it fits Tim's relationship to the bat team. Dick is blue, Jason and him are red, Harper and Babs are blue, steph is purple and Damian is gray.