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Go to https://www.skype.com/en/ in a web browser. Click Sign In. Click My Account. Scroll down and click Edit Profile. Uncheck the checkbox next to "Discoverability.
This is the Skype website where you can edit your profile. It's in the upper-right corner of the web page.  This displays a drop-down menu. It's the first option in the drop-down menu. If you are not automatically signed in to your Microsoft account, you will be redirected to a sign-in page.  Enter the email address associated with your Skype account and click Next.  Then enter your password and click Sign In. It's the first option below "Settings and preferences" at the bottom of the screen. "  It's the first option below "Profile settings".  This will prevent your Skype account from appearing in search results and suggestions.  This allows you to remove your account from public viewing without having to delete your entire Microsoft account.