Change your Skype id
Custom Skype name
No chance you can change skype ID. You can't even unlink skype from Win10.
My Win10 account is linked to foreign(not mine - somebody else profile) Skype account only because I have never used Skype in the past 10 years.
I have opened the case and nobody from microsfot nor Skype could help me, it cannot be unlinked.