For Windows :
1. Open the Run command/window (to open Run, just click the Windows Logo key in your keyword + R).
2. Type %appdata%skype into the Run window and click OK.
3. Delete the folder named after the Skype Name you wish to remove from the sign-in screen.
Example: If I want to remove account Username 1 in the login window, I just need to delete
the folder named Username 1 (screenshot sample below)
For Mac :
the location of the folder is;
User/Library/Application Support/Skype
where *User is your computer name.
The same process applies, just delete the folder named after the account username you want to delete from the login window.
Note: When you login again in the same computer, your username will re-appear in the sign-in window. you need to re-do the process again.
Skype Support link: Skype Support