This is not a suggestion I'm making for Tim, because it's a stoopid name, but Batboy hasn't been used in the main universe, has it?
For Tim a riff on the ornithological Robin is the obvious/predictable way to go, and a bird noted for intelligence possibly.
Owls, Crows, Magpies, Mynahs
Or maybe a new identity should go offbeat. Does he have a detective hero? other than Bruce obviously. Robin Holmes ha! nah
A potential storyline for Tim could be Owlman. He get's thrown into that verse shortly after owlman's death and takes on that role to take down the Injustice league.
"Wow. You made Spider-Man sad, congratulations. I stabbed The Hulk last week"
Wolverine, Venom Annual # 1 (2018)
Nobody does it better by Jeff Loveness
"I am Thou, Thou Art I"
Persona
This guy gets it. I've suggested this in other threads before. It sounds like a pulpy detective character from the early days of DC. Give him a fedora and crimson trench coat. Feature him in detective/private investigator stories.
That pretty clearly isnt the direction Bendis is going with his Wonder Comics though.
I mean, that's pretty close to the look I'd like for him. And you could also say it makes him sound too much like the avenger for the St Louis baseball team, but that wouldn't make me rethink it either I was aware office of Cardinal in the Catholic church when I first made the suggestion. I don't think it detracts from the name at all.
Either way though, the name lends itself to solo pulpy detective stories like Dick Tracy stuff. Tim seems to be going more towards the team leading youngster route. Name and look doesn't really fit that role.
There's always "The Buzzard."