Skype on my Android has been updated to version 4. Application has been completely redesigned. Skype says it's been "rebuilt from the ground up" to be faster and more reliable. Well, we will see :-)
Many user interface changes and speed improvements are welcome, but latest version of Skype has also some clumsiness. One of them is "hidden" SIGN OUT possibility.
But it is still there. If you are signed, tap the image on your avatar in the top right corner. That will open your account profile.
Then hit "the three dots" button in the lower right corner, or hit the menu button if your phone has it. Here you will find settings and sign out option.