Anonymity online has been a staple of the Internet community since it's conception, and although Google+ feels like it forcibly identifies you to the world, you can actually use it anonymously. One of my favourite tips for new Google+ users is to embrace the opportunity to be anonymous on it. You may be looking for gift advice for your someone's birthday and you don't them to find out. Or perhaps you're discussing something politically sensitive, and you don't want anyone to know your opinions. It could be something as innocent as wanting to write about something deeply personal, that Google+ Communities could give you support with.
[EDIT: Don't do this, as it may be against Google+ policies]
Create a separate Google account
The easiest way to be anonymous is to sign up for a whole new Google account. Google does not have any process for verifying that the name you use is correct and factual - the most important thing to them seems to be how your social graph works around you, so that you can get the right information at the right time. The main downside to this approach is that when you want to be in "anonymous mode", you have to logout and log back in (although you could try using Chrome profiles to get round this).
Creating a Page within your existing Profile
This option creates a Page for you, to which you can switch without logging in and out every time you want to switch to your anonymous identity.
1) First, go to your sidebar and choose Pages.
2) From here, you can click Create a page to begin setting this up. I've blacked out my anonymous identity, but you can see my Test Page here as an example.
3) For your category, choose Other.
4) Finally, choose your name and determine the appropriate age restriction for your Page.
To use Google+ as your new page, you just need to click on your profile photo in the top right.
