hi! this is a pretty popular question; not discouraging other responses, but you can catch up with previous posts here. Spoiler: TL;DR: no.

• FAQ section: Famous families descended from Roman families?

and some more recent & possibly better ones

• Did any roman patrician families survive the fall of the western empire? Is there anyone alive today that can claim to be a descendant of a roman senator?

• What happened to the Patrician bloodlines after the fall of Rome?

• Is there anyone who can trace their family tree back to a Roman family?

• How much did the Byzantine Empire change between the 6th and 15th centuries?

• Did any western European noble dynasty in middle ages originate from influential family in western Roman empire

also... it might be worth x-posting to /r/genealogy if you want more information about the availability of various types of records