I may be late, but here's the exact words from episode 79:
"HIS NAME WILL CONSIST OF THE NUMBER SEVEN, THE NUMBER GIVEN TO ALL REAPERS OF THE EAST, AND THE NUMBER FOUR... ...AND HE SHALL BE KNOWN AS "704.""
The number 4 is indeed a number relating to "death" in some East Asian countries, like Korea. We never really heard any other reapers getting called by their number names, so I think the creator just chose 04 for that reason.

Actually now that I’m thinking it, is there any significance to number 704? Was it addressed? Maybe we’ll get to know?