To request Google to remove your profile information follow the steps below.
Copy the Musixmatch URL you'd like removed from Google's index
Navigate to this page.
Paste in the Musixmatch URL that you'd like removed.
Submit your request.
Note: You may be required to log in to your Google account to complete the steps above.
If you don't have one, you may need to create one.
More information about removing your content from Google's search index can be found in this public removal form.