Since May, "anonymous" has been doing a lot of commenting. It was something Blogger was supposed to fix, in May, they said. Umm, not yet done. Having read the pages of what we can do--and finally semi-understanding it---I can offer some advice.
My offering computer advice is a joke in itself, so, if you prefer, you can go to the pages I read and decifer it for yourself. You will need to click on all the links provided, and each one offers more links.
Not having figured out the difference between Blogger and Blogspot, I will problaby interchange them incorrectly, but the info itself will work.
You start out with your Dashboard and all looks good, including your e-mail address at the upper right. You click on the latest entry from someone you are following, read it and want to comment. For some blogs you will see your name as one of the options, so you click on that, your comment is published and all is well. However, for most blogs, your name does not appear; instead, there are various options. Clicking on Google Account doesn't give the desired effect.
Look at the upper right of that person's blog. If your e-mail address is there, then you shouldn't have a problem, but if it says Create Blog, then something needs to be done.
There are three options, two of which you can do yourself; the third needs to be done by the blogger.
1) You can go to the top right of someone's blog and click on Sign In (next to Create Blog). This takes you to your Dashboard (or you can go there directly) and you click on Sign Out at upper right which will take you to the Sign In page. You think you're signed in--and you are--but not fully. Uncheck Keep Me Signed In.
2) You can "Allow Third Party Cookies" on your computer. (I'm somewhat iffy on doing this).
So, why and how did all of this "anonymous" posting come to be?
In June, 2008, Blogger started an Embedded Comment form. The people cheered. I found Blogger's explanation of what this is.
It must be the default for commenting because those whose blogs get "anonymous" comments have this type.
How to tell: The box for typing the comment will be under the previous comments and on the left when you are on the comments page.
Those who have other set-ups will have the comments box on the right (and your name will show as an option.)
I just changed mine to this because people were saying that they still couldn't comment as other than anonymous.
I sometimes pass on commenting to a blog cause I'm tired of being Anonymous!
What is happening is that Blogger is no longer able to authenticate because of the code changes they made in May, 2011. There was supposed to be a fix but it never came.
Thus, if you want people to be able to comment on your blog who don't allow third party cookies and who don't want to have to sign in each time, change the way your comments are set up.
Go to Settings, then Comments. Next to Comment Form Placement if you have "Embedded Below Post" selected, change it and save changes. I had clicked on Pop-Up Window but it jumped to Full Page. I have the most basic Blogger set-up so tht could be why.
For more info: http://blogging.nitecruzr.net/2011/01/technical-sophistication-of-your-blogs.html
Please feel free to mention it if you find any different information.