The very first thing we learn about R is that he doesn't have a name. "I can't properly introduce myself, but I don't have a name anymore" (1.1.1). The second or third thing we learn about him is that this makes him sad: "I miss my own [name] and I mourn for everyone else's, because I'd like to love them, but I don't know who they are" (1.1.7). None of his zombie friends have names, either, and this lack makes it impossible for R to truly love them. This is one of the main reasons he falls for Julie so hard: she has a name and knows it. Hey, if that's all it takes to fall in love, why aren't we all married with kids by now?
A lack of names isn't unique to the zombie community either. While in the stadium, R notes that "there are no names on the street signs" (2.2.4). All the street names have been replaced with symbols. Could these be so that everyone can find their way, regardless of language? Or is it a sign of everyone's dwindling literacy?
When R and Julie's lip-locking voodoo magic starts making zombies alive again, the Dead have to reintegrate into Living society. Step one to making them feel more comfortable? "Tell them your name and ask them theirs" (3.1.11). After all, can you call yourself a person if you don't have a name? And when in doubt, just make one up, like Marcus.