Given the messed up state of the timeline this is a very worrying question.
Convergance raises A LOT of questions on how pre-Flashpoint and Post timelines can be the same. Especially since Older Booster and Rip assumed they weren't. Rip told new 52 Booster who he really was ! Time travelers were considered valuable for their power and knowledge during Convergence. Rip was the only one who was able to avoid being caught because he kept his past a secret. But if Dr. Manhattan took ten years away wouldn't the Time Master know and won't they be a threat to him? Or the best source of information?
Booster Rider- Older Booster Gold who was dying thanks to years of (unprotected?) contact with temporal engery and was transformed into another version (the fourth?) of Waverider. Booster Rider would not just have a whole lot of power that's connected to temporal engery he'd liking learn a lot more. This version is said to be about 15 years older than new 52 Booster and Rip Hunter. He has the most experience so he'd be the one that Manhattan would want to keep an eye on.
New 52 Booster- Just after Flashpoint the last issue of the second BG series made it seem like this was the same Booster. Then Convergence happened and they said it wasn't. Now their saying he is? This Booster has a different origin and his sister Michelle is said to be dead. Despite not knowing who Rip Hunter was he somehow knew where the Vanishing Point was? He apparently never met his version of Ted Kord. This Booster was sent back to his home by Booster Rider.
Goldstar/Michelle Carter- The same Michelle from the Booster Gold series that apparently now knows Rip is her nephew. There isn't a living version of her in the new 52 world. She was sent away like the others by BR yet she showed up in Convergence with him. Unless Jurgens had her more trained she wouldn't be the go to person for information.
Skeets- We've only seen the new version that somehow knew who the Legion of Superheroes were. Rip says this version is more updated than his but it's unknown how Skeets can know this information. Or how much he does know. Unknown if the other version is still around.
Rip Hunter- He managed to avoid being captured last time and his dad made a big deal about keeping his sons' secrets. Rip did have a curious reaction when new 52 Booster talked about his world. In fact Rip wasn't familiar with it and seems to come up with some theories he didn't share. He did say that he suspected the new world was the most important one. For some reason his dad ignored him when Rip tried to bring something up and sent Rip away to protect him.
Mrs. Carter/Rip's Mom- We still don't know who she is but I'm assuming someone is with younger Rip since his dad is Booster Rider.
Little Rip- We learned that Older Boosters' son is 10, he'd be protected from harm and with his mother. He is pretty close to Jons' age.