What does Greg Norman have to do to lose the choker tag?

Whilst Greg Norman was undoubtedly a fantastic golfer and your points about him are valid, I think the answer to your question of what he needs to do to lose the choker tag is to win a major on US soil! Sadly, it looks to be too late for that now.

All Greg Norman needs in One Win, afer that he would have chance to win the majors.

Greg Norman may or may not deserve to be remembered as a choker but he should go down as the most talented golfer to only win two major championships. No other golfer in the history of the game "snatched defeat from the jaws of victory" as often or in so many ways as he managed to do.
He is the only player to have ever lost all four major championships in play-offs - the 1984 U.S. Open, the 1987 Masters, the 1989 British Open and the 1993 U.S. PGA. He is the only player ever to lead all four major championships after 54 holes in the same year and he went on to win only one of those. Now, these achievements don't necessarily make him a choker but we need to ask why his record in major championships (the events by which great players are judged) was so poor.
To use the argument that he was "robbed" by freak shots is both inaccurate and unfair. This happened only two times and only after Norman was unable to deliver the "killer blow" on both occasions.
In the 1986 U.S. PGA Norman blew a 4 shot lead going into the back nine and was tied with Bob Tway going down the 18th. Tway drove into the rough and did well to make the greenside bunker while Norman, with only a wedge from a perfect lie on the fairway (after his ball had landed in the rough and "luckily" bounced out) managed to spin his ball off the green and into the thick greenside rough. Any decent player would have, at the very least, put his ball reasonably close to the hole but he couldn't. This took all the pressure off Tway who then only needed a par to tie and his ball went in. Sure, it was a lucky shot but Payne Stewart did exactly the same thing about half an hour earlier.
In the 1987 Masters we all remember Larry Mize's terrible 5-iron approach to the 11th green. After a shot like that he deserved to be beaten but again, from the middle of the fairway and this time with an 8-iron Norman could only manage to put his ball 40 feet below the hole. Mize now only needed to get the ball close and we all know what happened. Norman seemed unable to deal with these situations, unable to go in for the kill. Instead, he seemed to take things easy and in the end he stuffed up.
In the 1989 British Open Norman began the final round with an incredible 6 straight birdies and got himself into a 4 hole play-off with Mark Calcavecchia and Wayne Grady. Norman was tied with Calcavecchia coming to the 18th and saw the American carve his tee shot into the long rough. Norman then inexplicably hit his driver down the short hole and found a deep pot bunker some 300 yards away. Even the Australian television commentators were aghast at the idiocy of hitting such a pointless shot. Again, as with Mize and Tway, Calcavecchia had all the pressure taken away and he hit a fantastic shot from the rough to about 6 feet.
Norman seemed incapable of analysing a situation even though he was a three time winner of the World Matchplay title. When it came to pressure situations his thinking seemed to go out the window. Is this choking, bad decision-making or just bad luck?
What happened to him at the 1996 Masters? It should have been a Norman procession to a wonderful and deserved victory but right from the beginning of the final round he played poorly and nervously. Why? Was it because he was paired with Nick Faldo? Was the sense of occasion too much for him? We will never really know but to squander a record 6 shot lead and shoot a 78 after shooting an opening round 63 is not the sort of thing a champion golfer would do.
By my reckoning Norman should have recorded at least 6 major championship victories, possibly even 9, which would have ranked him alongside some of the greats of golf, including Faldo, Ballesteros and Watson. Instead, he will be remembered only as a prolific international winner but with a major championship record equal to that of Andy North and Bernhard Langer.

You're kidding, right? "Just because he let a few winning margins slip by"? You mean the way E.J. Smith let a few iceberg warnings SLIP BY?

Greg Norman is known as a choker because he led the Masters by six strokes on Sunday, and lost it by four. That's called a choke, me bucko, and there ain't a thing you can say to make it anything different. And he's remembered for it because it was so... well... MEMORABLE.

Greg Norman is no longer the Shark but the undisputed Boss of the Loss.