The Big Boss Man, aka Ray Traylor. When he debuted in the WWF in the mid-80s under the guidance of manager Slick, he wrestled much like the Wrestling Monsters that were frequent in the time period. In fact, he even got teamed up with one, Akeem, to form the Twin Towers. The beard-growing period came for the Boss Man in 1990, when he split from Akeem and Slick and underwent a Heel–Face Turn. The next couple years or so saw him becoming more of a Lightning Bruiser in the ring, and an much beloved upper-midcarder. When he came back to the WWF in the late 90s, he'd grown the beard in terms of his on-screen persona (he went from the cop outfit to the SWAT-team getup), but he wasn't the in-ring worker he once was.
Daniel Bryan in the most literal way possible. He debuted clean shaven and wasn't much more than a jobber. He moved to Perma Stubble when he left NXT and a goatee when he won the US Title and MITB. He started growing it out when he became World Champ, but it wasn't til Team Hell No that he became a true star, when he stopped shaving entirely. By the time he was main eventing WrestleMania 30, he looked like a wildman from the mountains.
Dwayne Johnson began his pro wrestling career as Rocky Maivia, a one dimensional face in a time where people wanted something more. In short order, he made a heel turn, started constantly referring to himself in the 3rd person, took the mic and ran with it, and even main evented WrestleMania as The Rock. Now many consider him one of the greatest wrestlers of all time, and easily the most charismatic man in wrestling history.
Kurt Angle was always seen as a great wrestler, but people didn't start calling him the greatest wrestler of all time until he shaved his head after losing a Hair Match to Edge in 2002 (making this, in a way, a reverse Growing The Beard!). He got his first legitimate reign as champion later that year.
"Stone Cold" Steve Austin was originally given a gimmick of "The Ringmaster" and managed by Ted DiBiase. It was a pretty bland gimmick until he ended up losing DiBiase as manager in a match. Then he started getting himself involved with Bret Hart. He arguably grew his beard officially in an I Quit match at WrestleMania 13 when he refused to tap out to Bret Hart's Sharpshooter and passed out instead.
Anytime you put a wrestler in a hardcore match with Mick Foley, this will happen.
The Undertaker had grown stagnant as a wrestler, and hadn't wrestled an interesting match in years. Then Mankind shows up in 1996, and proceeds to take The Undertaker to the limit, now, both men are legends.
Triple H had recently won his second World Title from the Big Show, but fans didn't really take the guy as a serious champion. Most still saw him as Shawn Michaels' Depraved Bisexual cohort from DX. Until his matches with Cactus Jack at the 2000 Royal Rumble and his other match with Cactus Jack in a Hell in a Cell at the 2000 No Way Out. Through a combination of Nepotism and Executive Meddling, he has been the Villain Protagonist of the whole company for 14 years and counting.
Randy Orton was considered nothing more than a bland third generation wrestler who only got there because his dad was Cowboy Bob Orton. Kind of like how fans first responded to The Rock. After a feud with Mick Foley culminating in a match at Backlash 2004, he became a real main eventer, and beat Chris Benoit for the World Heavyweight Championship at the main event in SummerSlam four months later. Today, he's practically the face of the company.
Edge had already built up quite the midcard following thanks to the three-way feud between him and Christian, the Hardy Boys, and the Dudley Boys in the early 2000s, but most people didn't take him seriously as a main event talent, even with a blink-and-you'll-miss-it WWE title reign under his belt in early 2006. Enter Mick Foley again, and a hardcore match at WrestleMania 22, and suddenly Edge had become cemented as not only a main event talent and worthy champion, but a future legend. Destroying his "friend" Matt Hardy's career didn't hurt him too much either.
The entire industry of Professional Wrestling itself is one of the great American success stories, going from "soul patch" to "Greek Orthodox priest" in a mere three generations. A key splash of Minoxidil came in the 1930s, when Boston promoter Jack Pfefer started to move the image of the business away from "actual sport" to stylized, circus-style entertainment. But the beard really got bushy in the 1990s with the advent of Monday Night Raw: now the disjointed spectacle coalesced into a weekly soap opera with recurring characters and much more interesting storylines. The final touch, arguably, was Vince McMahon establishing himself as an on-screen villain toward the end of that decade, providing a sort of axis for his elaborate fictional world.