Unfortunately you cannot delete the profile.
BUT you can delete the biographical details and make the profile UNLISTED - which means it wont show up on searches. And the only person who will know and can access that profile, is you!!
Later on if you can reuse that same surname, but for a different (preferably dead) person, you could change the details for someone else in your tree with the same surname - and then change the privacy so that it can be seen.