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From Skype for Windows - start the Skype client, log into your account (if necessary), press the profile picture located in the upper left corner of the main program window and select the item Manage accounts.
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If you are going to act from the computer, you can change your name in Skype without creating a new account, acting directly from your profile settings, which can be accessed via the Web or directly from the Skype client for Windows and macOS. Let's see how to proceed both on PCs and on mobile phones and tablets.
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I guarantee that this is such an easy operation to perform, that there really would be no need to give you much explanation. Wants change public name in Skype, that is, what other users see.
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