Google+ demands users to use their real name for their profile (and it is not totally clear what a real name is for Google, as some users are blocked, others are allowed to have a pseudonym and so on).
Google+ is not the first platform to request this. Usenet is one of the oldest network based communication platforms, and the German speaking part (de.*) had (and somehow still has) a real name policy. It is/was considered polite to give your real name. Users were requested to use a proper name for their postings and some readers automatically filtered postings which did not have a proper author name. And it somehow helped.
For some discussion and legal background see Realname Diskussion (de).
Only reading postings where the author name consisted of at least two words and filtering single word names or names containing digits increased the quality of the postings. The reader is certainly not able to find out whether the name given is equal to the one written on the author's ID card, but this simple heuristics helped.
Facebook and Google+ require their users to use their real names. And it may also help. But I am not sure about this.
On the other hand there are a lot of people who have various serious reasons for not giving their real name (see e.g. http://my.nameis.me/, you will find a lot of other resources in the discussions on Google+).
Several people argue: this is G+F, not the Internet. There are enough places on the net where you can speak freely without giving your name, so if you need to hide you can. Just do not join G+F, this is company land where Google and Facebook set the rules.
On a first view they are right. G+F is not the Internet. It is like some private shopping mall. The owner may allow you to enter or throw you out.
And exactly this is the point: private shopping malls are destroying public space. You do not have the right to have some political demonstration or protest march in a private shopping mall, hand out fliers, ...
You can do this on public ground, but this will not help if no one is there because everyone is in the private shopping malls. Privatization of public space is silent removal of rights.
The Internet is some kind of public space. And social networks like G+F are part of it. They are a part, for a number of people an important part of their social life. So it is important that people who need anonymity have access to these areas, that they are not thrown out of the shopping mall.
The new Arabic revolutions are called »Facebook« revolutions (Twitter had an important part too), not Internet revolutions. These networks provide the connections, structures and tools necessary for most users to drive such kind of protest.
G+F is where the people are, so it is where the protest has to be, where free speech has to be possible without fear (of stalkers, the family, the boss, oppressive regimes, ...).
Using a pseudonym does not guarantee total anonymity, but it can help in several situations.
I am not too happy that these social networks (G+F and others) represent so much of the virtual social life of so many people. I am not happy that a small number of companies could step into the system at any time. I would prefer a much more robust, distributed, Internet-based architecture (yes, I know about Diaspora and others). But at least these large and important networks should not be allowed to say: »see, this is company ground you are standing on, we make the rules and you have nothing to say.« They are just too big and influential to do so. They are occupying too much of the social space (or at least will do so in the future if they continue growing).
Currently for most users the »Internet« is equal to WWW and email. There is more, but it is not recognized. For some users the Internet is the thing behind the Google search box. I have seen a lot of users who did not know they could write a URL into the address field, they type it into Google. And I got complaints because some of the URLs were not accessible this way. Most users know that there is something outside Facebook, outside social networks. Google will integrate a lot of services into Google+, from youtube to Google search. There will be something outside of G+F, but which parts of this free land will be visible to most of the users in the future (besides Amazon and porn)?
You are not forced to join G+F, you can stay outside (and I stay outside Facebook for several reasons). But this also excludes you from an area where social interactions happen, where social life is created and defined. Staying outside excludes you from an area which should be public space.
[UPDATE: see also drei elefanten (de)]
I like real names, so be polite and use yours if you feel ok with doing so. You may just filter or block users who use some silly nickname. The reader should filter, not the company, not the system.
But I feel that it is important to allow people in who do not feel good with or cannot use their real name. And as Google+ currently is beta and at least theoretically policies could be changed, I want to support those who feel the need to do so.
Henry says he has WLAN. He is neither on Facebook nor on Google+ until now. There are only few elks in virtual social networks.