Ten Ten is not the only character in this manga who has not been given a last name. There are more characters without surnames than those with surnames.
Jiraiya, Tsunade, Orochimaru, Gaara, Shizune, Temari, Kankuro, Nagato, Konan, Yaahiko, Deidara, Sasori and so many others....What are their last names?
I'm guess Shizune's last name is Kato since she's Dan Kato's niece. Tsunade's is Senju. Nagato is Uzumaki,