I have been consistent in saying that there is no one greatest player of all time, especially as the Open era has only been around for the last 45 years or so.
As for Sampras being the "greatest" or wanting to be known as "the greatest" then that is not possible. Federer has broken all of his records bar one and is still playing at a very high level at the age of 31.
When Sampras won the US Open in 2002 he should have kept on playing in my opinion, I thought that at the time. Also, Sampras knew the importance of the French Open, an extensive article / interview was done on Sampras in early 1997 (might still be on the internet I'm sure) where it was stated that Sampras needed to win the French to be considered the greatest. In fact, Pete Fisher was quoted as saying just that, apparently they would have arguments over dinner about that topic (this is before Pete Fisher had trouble with the law and went to prison).
Sampras' counter argument apparently was to state if he racked up the majors that would be as significant as not winning the French, so breaking the record became his obsession I suppose. As we know as well, Sampras' clay results took a real dive from 1997 onwards, when you would have thought they would actually improve as he was only 25 years old at the time.
Therefore I don't think Sampras can legitimately say he wants to be known as the greatest player to play tennis. He can legitimately say he is one of the greatest and put his name forward as one of the few players to play the highest level of tennis when in the zone.
We will never know but I often wondered how Sampras' clay results would have fared had Gullickson stayed alive and continued to be his coach until around 2000? He might not have won the French but perhaps he would have taken the clay tournaments more seriously and been much more committed to it 1997 and post 1997.