I find it strange that there are no remaining Roman gens left, not even in Italy, the heartland of the Romans. What happened to them, and why don't we seem to have modern corruptions of ancient Roman gens? Or did Roman nomens survive and we just never notice them?
What exactly are you asking? From an onomastic point of view, many gentes survive in modern onomastic material - Julius/Julia; Cornelius/Cornelia; Claudius/Claudia; Sergei (from Sergia); Emilio (from Aemilius); Fabio (from Fabius) and so on.
Personal names such as Marcus and Sex/Sixtus also do survive.
The geneological aspect would be a bit more difficult to answer.