When you sign in to Skype, your Skype Log-In name is saved automatically on the sign in screen top-down menu, only if you log-in successfully.

So to remove Skype name from the log-in screen follow the steps below:

For Linux users:

1. First of all you have to Quit Skype.
2. Then go to /home/YOURLINUXUSERNAME/.Skype.
where YOURLINUXUSERNAME needs to be replaced with your Linux user account name.

3. In the .Skype folder, delete the folder with the Skype User Name out of which you don't want to see in top-down menu of Skype.

OR

1. Some time the Linux system doesn't take you to the appropriate place through cmd as files you are searching for may be hidden so, if you cant find the .Skype folder in your home folder, press the Ctrl+H key combination on your keyboard to make sure you can see the hidden files and folders.
2. Now, find the folder with Name Skype and get inside it by clicking on that folder, and in that folder delete the Skype User Name folder which you don't want to see in top-down menu of Skype.

When you restart your system, The Skype Name folder you removed from home earlier will no longer be displayed on top-down menu of Skype.

For Windows user's:

1. First of all you have to Quit Skype and make sure that Skype is no longer running.
2. Click Start, type "run" and press Enter. Or press start and H key combination, it will take you to run cmd.
3. Type %appdata%\Skype there and click OK.
4. Now Delete the folder with the Skype User Name you don't want to see in top-down menu.
 

OR

1. Some time the system doesn't take you to the appropriate place through cmd as files you are searching for may be hidden so, if you cant find the .Skype folder in your home folder, press the Ctrl+H key combination on your keyboard to make sure you can see the hidden files and folders.
2. Now, find the folder with Name Skype and get inside it by clicking on that folder, and in that folder delete with the Skype User nNme folder which you don't want to see in top-down menu of Skype.

When you restart your system, The Skype Name folder you removed from home earlier will no longer be displayed on top-down menu of Skype.

For Mac user's:

1. First of all you have to Quit Skype and make sure that Skype is no longer running.
2. Open Finder.
3. In the menu bar, click on Go To Folder.
4. The Dialog box will appear, In that dialog box you have to type ~/Library/Application Support/Skype and click Go.
5. Now Delete the folder with the Skype user name you don't want to see in top-down menu.

When you restart your system, The Skype Name folder you removed from home earlier will no longer be displayed on top-down menu of Skype.