One of the most obvious ways to achieve anonymity - and one of the least useful - is to not publish your name, in your blog posts.
Edit the "Blog Posts" gadget, in the dashboard Layout wizard, and de select "Posted By".This solution will immediately remove your name from any posts published by you - as long as a dynamic template is not involved.
The dynamic templates, as with the blog posts newsfeed, do not reference the "Blog Posts" selections. This will be a problem, for achieving anonymity.
No blog, even with the "Posted By" option un checked, will be anonymous - if you publish a blog posts newsfeed.
This is the URL of this blog.
Now, checkout my anonymity test blog - in non dynamic view.
If you truly want to publish your blog anonymously, there are several issues which you need to consider - all of them necessary. The "Posted By" option is not part of these issues - since it has no effect on anonymity, in the blog posts newsfeed.
Having considered all of the issues required to achieve anonymity, consider the issues where true anonymity can be a problem. Blogger supports our right to publish our blogs, anonymously - and will not break our right to anonymity.