The original Reverse Flash was Eobard Thawne, AKA Professor Zoom. He was the nemesis of the second Flash, Barry Allen. Barry Killed him after he killed Barry's first wife (turned out she just had her mind warped into a new body in the 30th Century the moment before she died, but Barry didn't know that until later) and was about to kill his new fiance on their wedding day. He would continue to appear occasionally anyway because he's a time traveller from the 25th Century and sometimes he, from before he died, travelled to some point after he died, and fought the Flash there. Also, there was one notable time when Abra Kadabra, a villain from the 64th Century, thus much more powerful than Professor Zoom (who at that point got his super speed with tech from his 25th Century future, though later he would instead make a connection with "The Negative Speed Force"), disguised himself as him just to fuck with Barry, but it accidentally just got Barry acquitted of the murder of Thawne because now everyone thought he was alive again even though he wasn't. Later, Barry died and his sidekick, Wally West, got promoted from Kid Flash to regular Flash, and eventually another guy, Hunter Zolomon, fashioned himself into the new Reverse Flash, with a similar costume and such, and was also called Zoom, but not Professor Zoom. Eobard Thawne got the nickname The Professor because he was a brilliant criminal genius or something. He was deliberately fashioning himself into Wally's nemesis and a replacement for the old Reverse Flash, but I guess he wasn't pompous enough to go around calling himself Professor.
The first Flash, Jay Garrick, also fought a villain called The Rival, and later he was retroactively considered a Reverse Flash, but he isn't really as similar as Thawne and Zolomon.
Nearly 25 years after his death, Barry came back to life. Shortly after, so did Eobard Thawne, but Barry probably didn't expect this, since Thawne was dead for like 30 years by this point. However, he didn't discount it could be him or some other Reverse Flash, like perhaps Zoom.
>tl;dr: There are multiple Reverse Flashes. Each one has a real name and an alias. You could consider each to have multiple aliases. Eobard Thawne is also known as Professor Zoom, also known as a Reverse Flash, also known as The Reverse Flash. Not to be confused with Hunter Zolomon, AKA Zoom, also a Reverse Flash, also referred to as The Reverse Flash when he was the most relevant one.