It is conceivable that he is in fact the proprietor of the establishment and his name is Hampton.
In any event, the man is clearly devoted to his trade: After witnessing Max's apparent murder at the hands of KAOS agents Stromberg and Christopher, he has the presence of mind to make sure Max is dead before cancelling his lunch order [Episode #34: "The Only Way to Die"].
On another occasion, Max, momentarily besotted by the madcap heiress Tracy Dunhill, describes her as "fascinating and beautiful". The waiter thinks he is talking about the salad, adding "... and very low calorie" [Episode #45: "Kiss of Death"].
When Max is understandably acting paranoid due to a $250,000 bounty place on his death by KAOS, the waiter is one of several acquaintances he suspects of trying to collect, demanding to know what he has in mind for the knife he is carrying. The waiter replies that it is for another customer's steak [Episode #47: "Someone Down Here Hates Me"].
[Despite having a speaking part in three episodes the part of the waiter remains uncredited.]