Hopefully, I have it figured out. I got the information, not from Google---and shame on them---but from doing a search and reading blogs of those who also have had problems commenting this week and/or have temporarily lost their Followers.
If you are signed in every blog you go to should show your e-mail address at the upper right, but this week it has shown Create a Blog and Sign In. When I went to comment, instead of showing my name, it said to select a profile. When doing that, a page came up asking me to Sign In. I quit there but I guess some got caught in the loop of this.
Bloggers suggestions were to Sign In and uncheck the Keep me Signed in box (not certain of the exact wording). I heard some had trouble signing in in the first place, but since I was already signed in, this second signing in should not sign me out when I left the site. Confused yet? It did work because when I went to comment on a blog my name did show up.
It's crazy when trying to comment on my own blog my name came up as Anonymous, but, fingers crossed, hoped I have solved the problem.