Mexican promotion AAA was the first federation of moderately well known luchadors Psychosis and La Parka. When the two had a falling out with AAA and left, AAA sued them for the gimmicks and gave the Psychosis and La Parka gimmicks to different wrestlers to play. The original La Parka (Adolfo Tapia) did something of a reverse Other Darrin by keeping the gimmick but changing the name to LA Par-K. The original Psicosis (Dionicio Castellanos) uses the Nicho El Millionario gimmick in Mexico outside AAA.
There was a short lived running gag involving Los Payasos, a stable of 3-5 clown luchadores whose only difference was the hair color on their masks; as Mexican tag team matches require the leader being pinned/submitted to win they would all change their masks in the middle of a fight so they all would have the same as their current leader forcing the opposing team to pin/submit all of them.
In WWE, the role of Doink the Clown was given to several other wrestlers following the departure of Matt Borne (who played him first) until it was given to Ray Apollo (who played him until the character was phased out). Ironically, as all this was going on, Borne continued to play Doink for several weeks in his new home, ECW, as part of a storyline that led to his new character, Borne Again. Doink has also been played by Dusty Wolfe and Steve Lombardi, and a whole host of wrestlers have donned the costume temporarily as part of angles.
This is also currently being done in TNA. The character of 'Suicide' was supposed to be played by Frankie 'Kaz' Kazarian. Kazarian injured himself, and, since the character wore a full-cover bodysuit and mask, the role was given to Christopher Daniels. When Kazarian came back, TNA worked the switch into the angle, with some of the other wrestlers accusing Daniels of being Suicide.
Now there's a third Suicide — Kaz has returned to competing under his old name with no explanation, while Suicide is now being played by Kiyoshi.
TNA managed to take it up to five wrestlers before the presumed end of the character. Suicide disappeared for about two years, and came back with TJ Perkins under the mask. He received a title shot, and won, at which point Perkins was revealed as having been attacked before the match, and a different wrestler was under the mask. On the following episode, that man, the X Division Champion, was revealed to be Austin Aries.
A promo following this tried to handwave it off as having been TJ Perkins all along. Oddly enough after this, Perkins would keep the Suicide outfit on during matches but with slight alterations and going by "Manik". Backstage he appeared with the mask off. When he had a heel turn he kept the name but got an entirely new un-Suicide related outfit.
When Kevin Nash and Scott Hall — who were billed as Diesel and Razor Ramon, respectively — left the World Wrestling Federation in 1996, Vince McMahon decided that (because the characters were trademarked, and thus, legal property of the WWF) he would recast Diesel and Razor Ramon. Hence, Glen Jacobs would perform as "Diesel" (one of Jacobs' many pre-Kane roles), while Rick Bogner became the new "Razor." Of course, it was obvious to fans these were Other Darrins performing these characters, and not just by lack of ability, but by overt explanation by the WWF announcers (including Jim Ross, who briefly turned heel as part of this gimmick). The "Fake Diesel"/"Fake Razor" storyline proved unpopular and was soon dropped; Bogner left the WWF not long afterward, but Jacobs was repackaged as Kane ... and the rest is history.
Ric Flair took the role as the Black Scorpion in 1990.
Flair only appeared as the Black Scorpion in its final appearance, when he was unmasked. Previous appearances of the Black Scorpion were handled by other guys.
Ultimo Dragon, after receiving his release from WWE, unmasked because there was talk of WWE bringing him back sans gimmick under his real name, Yoshihiro Asai. That never panned out, and for some reason Asai couldn't just go back to being Ultimo Dragon, so he became the latest incarnation of Tiger Mask. In the short lived promotion DragonDoor, Asai participated in a real vs impostor angle that made the Undertaker/Underfaker angle look good. Second Dragon, Dragon the Great, Tiger the Great, and all sorts of imposters were running around the promotion, and to keep things more confusing Asai would switch from being Ultimo Dragon to Tiger Mask to Tiger Dragon all in the same card.
When TNA decided to do an ECW reunion show called Hardcore Justice they wanted to bring back as many people from the old ECW as they could while Writing Around Trademarks, most of the guys used their old character but there were 2 indie wrestlers given old gimmicks to use both were kind of strange choices for different reasons:
The Blue Meanie was played by Big Tilly who has worked off and on for TNA for the last half decade. While this normally would not be that bad (as the two bear a passing resemblance to each other, and Meanie was a big part of the bWo who are essential to any ECW reunion), but the problem was they showed the real Meanie (Brian Heffron) earlier that night in a pre recorded segment. Al Snow even pointed out that it was a different guy despite Nova insisting it was the original. Incidentally, the trope was invoked when Stevie Richards thought it was a little weird to have a fake Meanie — Nova launched into an explanation involving Bewitched and the two Darrins.
The other replacement was Lupus, who was portrayed by an unknown named Sam Shaw. This was strange because not very many people (even die-hard ECW fans) remember that there even was a Lupus — he only lasted about a month as a minor member of Raven's Nest, and only wrestled 2 matches!. Really, the Gigolo would have gotten a bigger reaction then him even if it was the real Lupus.
Shortly after his WWE debut in 2011, the wrestler behind the Sin Cara mask, a luchador formerly known as Místico, failed a drug test and was suspended for 30 days. In order to keep the character from losing momentum, WWE developmental talent Hunico was brought in to wrestle under the Sin Cara mask until Mistico's suspension was up. This was then turned into a storyline with Hunico wanting to take over the role of Sin Cara. This because at one point, Hunico had used the name Mistico but with a different gimmick, but lost the right to use the name to CMLL who had given it to the man who now portrays the Original Sin Cara, and the two entered a feud over who will be the "real" Sin Cara. In the end the original Sin Cara won a Mask vs Mask match, kept his mask and name, while Hunico is competing without a mask.
Later when it appeared clear Sin Cara wasn't re-signing, they gave the Sin Cara gimmick back to Hunico and he has been Sin Cara ever since sorta karma-like. However even then the first Sin Cara, couldn't go back to his old moniker of Mistico because CMLL ended up passing it on to another wrestler when he left. So now he is Myzteziz.
Randy Colley (aka Moondog Rex) was the original Smash of Demolition and he claims to have come up with the gimmick. At the TV tapings for Demolition's first matches, which were done in WWE's home region of the Northeast, some of the fans recognized Smash as Moondog Rex and actually shouted "Moondog Rex" during the matches, rendering it impossible for Colley to continue under the gimmick. Barry Darsow replaced Colley as Smash and the rest is history.