We can solve this issue by going mobile settings then application menu. In application menu select installed apps then tap on skype, other menu will show clear cache and data and run skype. All previous username and passwords will be deleted and you can use your other id to sign in.
Skype is online calling app to make free calls all over the word from skype to skye on internet. Some android phones creates problem when we want to log out skype and want sign in with other account. But previous id not log out even we have log out or turn of wifi. When we restart device and run skype it won’t sign out and remain signing in previous id.