04-08-2011 19:17 - edited 04-08-2011 19:20
Click on the profile button in the upper left hand corner and then the signout button on the screen that pops up.
It's not the Tags screen the top arrow is pointing at, it's the Profile button at the top of the nativation bar (or whatever Skype is calling the vertical bar on the left).
If that's no help, sorry, I hope someone else will do better.
This happened to me too - the profile column g4pilut shows in his screenshot had completeley disappeared.
It reappeared once I switched off the iPad, and then switched it on again. I could then logout as before.
(You may not have to switch off entirely - maybe just exit the app using the options that appear if you click the home button twice.)
Looks like a flaw in the app.