Privacy concerns
In a requirement that has generated some controversy, Google insists on real names instead of pseudonyms, as people use on many websites to hide their identity. One of the reasons for this is that Google wants users to have verified identities, both privately and publically.
Here's the start of how Google expresses this policy, as follows (see http://www.google.com/support/+/bin/answer.py?answer=1228271):
Using real names is an attempt to (as Google states in the preceding material) make the site more like the real world, where you can find people based on the name you know them by. It also cuts down on nastiness and incivility (flame wars) often seen on sites where individuals hide behind concocted user or screen names.
This is not an unusual concept. Facebook started out by suggesting that real names be used and this is still very common on that network.
In the long run, it's quite possible that, due to pressure, Google will relax this policy. I suspect this will eventually be the case, but for the time being, use your real name or risk getting kicked off. That's the way it is.
Personally, I've been on the Internet pretty much continuously for decades and always used my real name, and will keep on doing that. As a writer, I make my living by having people know who I am.
I realize others have privacy concerns about putting their real names on the Internet, so you'll have to make your own choice in this matter.
Mine is: Real names are okay and Plus is fantastic.