Thank you all who voted for this request! We have recently made changes which should allow you to see your Username. On Skype 8 You can see it in Settings > Account & Profile under Skype Name field.
In case you created an account using email or phone number you will see your username as live:emailid or live:uniqueidentifier.
No exact release date is available but we are working on adding support to allow users to customize their user name. I’ll keep you posted as we move closer to release
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I legally changed my name. I can update everything else in my life, but not Skype. Social security, credit cards, driver's license, deeds and titles, mortgage, passport, employment records, insurance policies, every online account and service... but not Skype. >:|