Can I keep my mother's last name as Muslim?

I would like to seek your guidance on a naming matter in Islam.My Mother asked whether it is permissible to use her last name instead of my father’s. My mother gave me that last name as Sultana, which is also my Mother's last name, but we both are trying to understand Islam better. Could you please clarify the Islamic ruling on this? Jazakum Allahu Khairan.