To delete your profile details:
For Windows, go to Skype > Profile > Edit Your Profile...
For Linux, click on your Skype Name above your contact list and select Edit profile.
Then remove all the information in your profile.
To delete a Skype Name from the sign-in screen:
If you are using Windows XP:
Quit Skype. In the system tray at the bottom right of your screen, right-click the Skype icon and select Quit.
Click Start > Run.
Type %appdata%\skype into the Run window and click OK. All the files held in the Skype folder in your Program files appear.
Delete the folder named after the Skype Name you wish to remove from the sign-in screen.
If you are using Vista or Windows 7:
Quit Skype. In the system tray at the bottom-right of the screen, right-click the Skype icon and select Quit.
Click Start. In the blank field that appears, type run. Press the Enter key.
In the Run window that appears, type %appdata%\skype and click OK.
All the files held in the Skype folder in your Program files appear.
Delete the folder named after the Skype Name you wish to remove from the sign-in screen.
If you cannot see the folders mentioned above, it may be because they are hidden folders. To make them visible, press CTRL + H.
If you are using Linux:
Quit Skype.
Go to /home/YOURLINUXUSERNAME/.Skype and delete the folder with the Skype Name you no longer wish to use.
Now start Skype. The Skype Name you have deleted is no longer available on the sign-in screen.