But, yes what you have asked for is possible from now on, and is what I do for a number of my blogs.
Firstly, if you're using the standard the About Me or profile gadget then remove it. (Make your own with an HTML gadget or something if you really want to.
Make sure that you only ever create posts using account B.
(NB This was a change a little while ago: for a long time, the author was set to the first account that hit Publish on a post. But now it's the first account that saves the post. To be safe, in case they ever change it back, you would be best to make sure that Account B does all the publishing too.)
Give Account A whatever rights you want, and use it to do anything except creating or doing the first Publish of a post.
The only thing you cannot do is to remove Account A's name from posts it may have already published. (i've suggested a work-around for this here, but it's a bit messy.)
Sidenote: you shouldn't have two Google+ accounts: each natural person is only allowed one according to their Terms and Conditions. However its fine to have two Google accounts, with only one of them having G+. (You could think of the other one as a G- account :-)