Just because I always find it interesting. There were a few different meanings to some of these. Do the names fit the characters ?
Damian- To tame. From the Greek name Damianas, "one who tames, subdued."
Wayne- Craftsman, Wagon maker, wagon driver.
Does it fit?: Damian definitely does fit, Talia wanted Damian to tame the world but at present he tames animals. I don't believe Damian has a middle name. Wayne doesn't work as well unless you think "wagon driver" means he's in charge or take into account that the Waynes crafted Gotham. The two names do show a difference between the two families.
Richard- Powerful, Strong Ruler
John- God is gracious.
Grayson- Son of a Steward, son of the grey-haired one.
Does it fit?: Dick is known for being a great leader. John is after his father and unlike him Dick was lucky enough to survive. I found a couple different meanings for Grayson but it's kind of moot since the connection to the Court of Owls had this as a fake name. Cobb gave his son this name after giving him to Haly Circus because he was the "Gray Son."
Timothy- God's honor, honored by God.
Jackson- God has been gracious, has shown favor.
Drake- A male duck. Also a type of Dragon.
Does it fit?: Much like Dick he's another Robin that has a lot of respect and love from the superhero community. I guess you could say Tim has been honored by God. Jackson seems to be a nod to his father Jack (I don't know if this has returned to his middle name.) The duck example has played into Futures End where Tim owns a bar called the Wounded Duck after getting injured.
Jason- Healer, to heal
Todd- Fox. A clever or wily person.
Does it fit?: It fits brilliantly. Jason isn't just trying to heal himself after his ordeals he's trying to help others like Bizzaro. Curiously Peter isn't a name Jason gets from his dad, although not everyone gets their middle name like that. It's a good way to highlight his determination though. Besides the Zorro comparison I made Todd works in another way since Lobdell is highlighting Jason's mind. We've seen his cleverness in UTH and he's managed to use his smarts to get the upper hand on Batman. He's wily by being undercover and some of the tricks he's pulled to com out on top.