i dont know where he got the idea, but he called himself "The Rated-R Superstar" after his feud with matt ended, cause he was having a REAL LIFE affair with Lita, while edge was married and lita was dating matt at the same time, heres the entire story i found of wikipedia...
It was around this time that Edge came under heavy criticism, especially from the Internet wrestling community, due to the affair he had with Lita, the girlfriend of his close real life friend, Matt Hardy, who Matt had been dating for six years. Hardy had been out of action for several months with a torn anterior cruciate ligament and shortly after he recovered, Lita suffered the same injury and was put out of action. It was during this time that Edge, despite being married, began an affair with Dumas while she was still in a relationship with Matt Hardy. Shortly after the incident became public knowledge, WWE released Hardy. After Hardy returned, the real-life situation was translated into a storyline [7].
Nevertheless, or perhaps because of this, Edge was paired with Lita in an angle where she turned on her storyline husband Kane. On the July 11 edition of RAW, Edge's match with Kane was interrupted when Matt Hardy made a surprising appearance. The situation was a worked shoot, with Hardy referring to Edge as "Adam" and issuing a threat to Lita as well. When Hardy was officially brought back to RAW, he and Edge continued their feud, including a match at SummerSlam 2005 where Edge defeated Hardy in a match by causing Hardy to have "excessive blood loss." They also competed in a Street Fight, which resulted in a no-contest when Hardy performed a Side Effect on Edge off the entrance ramp into the sound speakers and other electrical equipment. They also fought in a Steel cage match at Unforgiven 2005 that Matt won after a leg drop on Edge from the top of the cage. The feud culminated in a "Loser Leaves RAW Ladder Match" at WWE Homecoming which Edge won, causing Hardy to move to SmackDown!.
Shortly after the Homecoming victory, Edge suffered a (legit) torn pectoral muscle that kept him shelved for several weeks [8]. During his time off, he starred in his own talk show segment on RAW entitled The Cutting Edge and dubbed himself the "Rated-R Superstar". Edge used his talk show to start a feud with Ric Flair following Flair's well-publicized arrest in connection with a road rage incident. Edge began using "The Cutting Edge" as a soapbox to run down Flair until, after weeks of public mockery, Flair eventually showed up and attacked Edge.
i guess, he called himself "The Rated-R Superstar'' because hes oversexed