Currently, when a user posts a blog, the author's name is shown as the login name. Is there a way to show the full name instead?
There is a setting enabled in the admin console that says "Show the full name of blog authors" but looks that that's not it.
Has the author filled in that information under My Settings > Personal Information?
In addition to having their name entered in their profile and the admin setting you mention to show full names, the authors also need to have the BlogAuthor role in order for their full name to appear.
So, for the blog(s) in question, select Blog Admin > Users > Roles > Click List Users for the BlogAuthor role and select the users whose full name you wish to appear against their articles. I admit this is not an obvious step to take but hopefully this should answer your query.
Please let me know if you still have any questions about this.