Well, it doesn't really matter how you romanize it, since it's pronounced dzu, or zu or whatever. I'd imagine the use of "du" is a result of the way the kana are organized. Most of the kana in Japanese are organized into groups of five with the same consonant and each of the five vowels, such as "ka ki ku ke ko," "ma mi mu me mo," etc. Of course, there are lots of random exceptions, like "sa shi su se so" and "ta chi tsu te to." However, in a certain sense, these are still considered "ta ti tu te to," they just have idiosyncratic pronunciations. This is also probably why Japanese people say "tsu" when saying the English word "two," even though they can easily pronounce hard 't' sounds.
Also, when you add the little two comma shaped radical as mentioned above, the sound becomes voiced (this is a linguistic term for using your vocal cords to pronounce a consonant). In this way, "ka ki ku ke ko" becomes "ga gi gu ge go" and "ta ti tu te to" becomes "da di du de do." Of course, since the 't' line is irregular, this actually becomes "da ji dzu de do."
Anyway, the point is that zu and du are both approximations of a sound that is a voiced tsu. I'd favor the dzu spelling, but it's not exactly common, in which case zu is slightly better because it's a bit closer than du. However, in official romanization systems, which the creators of Melty Blood probably used, it's spelled du to fit in with the pattern of the kana. 'shi' is also sometimes romanized as 'si' for the same reason, but since the sound is more common the more intuitive spelling has become preferred.
On another note, Yumidzuka is really composed of 'yumi' and 'tsuka' but consonants in Japanese tend to get voiced in compound words. The same thing is seen in words like origami, which contains the familiar 'kami' for paper.