With Blogger (Google), as with most Internet services, there is no real proof of identity required. In the online world, many people maintain multiple identities. That is one of the features of online life, called "freedom". Freedom to be who you want to be, or at least to seem to be.
So you, and I, can have as many Google accounts as we wish. Google accounts are free, and if you have multiple lives, or interests, you can have a different Google account for each, and more. And therein lies a problem.
Occasionally, someone asks about having a publicly accessible blog, but blocking specific individuals from accessing or commenting upon the blog.
How do I block one person from accessing my blog? I want it to be otherwise publicly accessible.but that's an impossibility. Since nobody is restricted to having one identity, if you block one identity from access, it's no great effort for someone to use another. Any determined attacker won't be put off by one identity being blocked, though he may be slightly angered, and his next series of attacks may be nastier than before.
If you're going to restrict access to your blog, you have to start with a private blog. That's the only real solution for restricting access.