While the Reverse-Flash was certainly different, he may have earned the name in a way Eobard Thawne hasn't. The origin story for Barry Allen's revamped nemesis revealed how the villain took the opposite gimmick to its most obvious extreme.
For years, Thawne tormented Barry and did everything he could to destroy his enemy's legacy. However, it seemed that Reverse-Flash and Flash's rivalry came to a bloody close when Thawne was killed by Thomas Wayne at the conclusion of Flashpoint. While Barry was temporarily freed of his twisted nemesis, a new Reverse-Flash appeared in the New 52 to challenge the Fastest Man Alive with powers that countered the Flash's speed. Unlike Eobard Thawne, this new Reverse-Flash's identity was set up as a mystery for Barry to solve as he chased down a killer who had the ability to target people connected to the Speed Force.
However, Barry discovered that the new person to take on the Reverse-Flash moniker is, in fact, Iris West's brother Daniel. How Daniel became the latest person to take on the villainous legacy is revealed in The Flash #23.2 by Francis Manapul and Brian Buccellato. Shortly after Daniel was released from prison, the Flash’s Rogues set up a scam during the chaos of Gorilla Grodd’s invasion of Central City. Pretending to aid fleeing citizens, the Rogues took a bus into Mirror Master's Mirror World and robbed the engers as a 'repayment' for their service. Daniel refuses to play their game and hijacks a car he finds in the Mirror World, only to crash into a monorail that possessed a Speed Force-powered battery. The fusion of mirrors and the Speed Force causes Daniel to emerge from the wreck with powers that work opposite of the Flash's.
Eobard Thawne was the first to discover that got Speed Force powers that literally were the opposite of Flash, thanks to West's accident in the Mirror World. Not only does the origin justify the name 'Reverse-Flash,' it finally gives Barry an evil counterpart whose speed was made to work in a way Flash's doesn't.
The New 52 was insistent that the Speed Force accrued power by moving forward in time, so giving Barry a foe that gained strength by going backwards was pretty inspired. Though the Flash hasn’t been haunted by West since the early days of the New 52, this Reverse-Flash more than earned the name.