Back when that chapter came out the accepted theory was that Oda was referencing the chinese naming taboo culture.
So the D. was name they did not reveal to others, and Water was a "publicly" known name but one that shouldn't be used much.Why Oda decided to use such naming convencion only for Law remains a mistery, could just be that he wanted to use the WaterLaw/Waterloo pun or he could actually be hinting at some more family story for Law.
Cool that it was talked about here. On OJ, people thought it didn't matter when this came out