I understand I cannot change my Gmail account name. I have a blog on Blogger and want to change the account name for it. Can I do it? And if yes, how?
Yes, you can transfer control of it to another Google account.
In short: to do this, make the other account into an author (Settings > Permissions, add). After the other account has accepted your invitation, go back to the Settings > Permissions screen and make it an administrator. Check it works, then use it to remove the administrator rights of the old account. This is the basic transfer procedure - and it's a good idea to do it using a different browser for your old and new accounts.
But there may be other things you need to change, too, depending on how your blog is set up, and what features you've used. I've described a lot of them here: http://blogger-hints-and-tips.blogspot.com/2010/01/transferring-blog-ownership.html