In Skype, click or tap your name and your profile will be displayed.
Select your display name in your profile. An edit box appears. and you can change your display name .
Type the name you want to use and select the tick button or press Enter. Your display name will be updated.
( 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.
In Skype for Windows desktop, you can also change a contact’s name: just right-click on it in your contact list and choose Rename. This only changes the name in your Skype, not theirs. )
PS : google is your best friend for such problems
but i hope this helped.