Actually, we could use a bit more info. Are you unsure of where to log out, or is it that you've found where to log out, but it's not behaving correctly?
If it's the first thing, you can log out by clicking on that gear icon in the top menu (which takes you to the settings page), and then hovering over that same gear icon and clicking on "Log Out".
If it's the second thing, you've likely got some weirdness with your browser cookies, and you might want to clear them out via your browser's privacy options. In Firefox, go to Tools > Clear Private Data, and select "Cookies". You can also go to Tools > Options > Privacy > Show Cookies, and just delete the ones from telltalegames.com if you'd prefer. In Internet Explorer, go to Tools > Internet Options > General > (under Browsing History) Delete... > Delete Cookies .
I erase my cookies pretty regularly and can confirm that's correct. Not that you shouldn't believe what Telltale employees say, they tend not to say things they're not sure of.
Comments
If it's the first thing, you can log out by clicking on that gear icon in the top menu (which takes you to the settings page), and then hovering over that same gear icon and clicking on "Log Out".
If it's the second thing, you've likely got some weirdness with your browser cookies, and you might want to clear them out via your browser's privacy options. In Firefox, go to Tools > Clear Private Data, and select "Cookies". You can also go to Tools > Options > Privacy > Show Cookies, and just delete the ones from telltalegames.com if you'd prefer. In Internet Explorer, go to Tools > Internet Options > General > (under Browsing History) Delete... > Delete Cookies .
Hope this helps!