Musixmatch Pro allows you to change your artist name and display a stage name different from your legal name, so your First name and Last name will not be displayed.
Head to Musixmatch Pro
Click on your profile picture
Click on "Manage profile"
Click on the icon next to "Personal info"
Add your Stage Name
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Not only you can add your stage name, but you can also select the option to hide your legal name in every Musixmatch public content.