Jeff,
I know what you mean, but need a little more information. There's a bit of thought that goes into all the different connections, so I'll try to explain them as best I can.. if you have other questions or suggestions, we're always up for them.
The SCLogin module will only display the avatar from Facebook or LinkedIn. The priority of which is an option in the SCLogin parameters. If it's set to LinkedIn, but the user doesn't have a LinkedIn account but has connected with Facebook, we'll show their Facebook avatar instead. We don't (but likely will add) an option to display the avatar from one of the 3rd party components we integrate with (CB, JomSocial, Kunena, etc). That will then either be a custom avatar the user uploaded, or the one that has been imported from Facebook/LinkedIn.
As for the name, where are you seeing the name? If it's in the SCLogin module, the "Welcome Joe" text, that's configurable again in the SCLogin parameters as either "name" or "username".
My only guess is that when you logged in with LinkedIn, you created a new account. LinkedIn doesn't allow us to 'see' the user's email address, so we can't match things up automatically like we do with Facebook. Can you check if you possibly have 2 users on your site: Joe (Correct Name) and Joe Tester?
Again though, feedback and suggestions are welcome. While creating JLinked we ran across a lot of priority/precedence issues and tried to do what we could on an automated basis. More work is definitely to come though.
Thanks for your input!
Alex