Your Skype name is the username you created when you first joined Skype, other than your email address or phone number. If you sign in with an email address instead, then you have a Microsoft account, not a Skype Name.
Also, what is your Skype ID?
To find your Skype ID on Windows, simply select your profile picture, and your Skype name will be displayed in your profile. For users that sign in with their Microsoft Account, they will not be able to find their Skype ID there, but the email address of their Microsoft Account instead.
Can you change your Skype name?
In Skype, click or tap your name and your profile will be displayed. Select your display name in your profile. An edit box appears. Remember, your friends might change the way your name is displayed in their Skype contact lists, so the display name you choose for yourself isn't necessarily the one they see for you.
How do I find out what my Skype name is?
—Click your profile icon at the bottom left of the Skype for Windows 10 window. —Your Skype name is displayed in your profile. —Tap the My Info tab and you will see your Skype name displayed beneath your full name in lowercase letters. —Click your profile picture in the top left of the screen.