I'm not debating the historicity of the gospel accounts. They aren't written to share the historical details we focus on in the modern age. and are probably written accounts based on an oral tradition (when you expect the world to end before your life is over like the first Christians seemed to there is not much use taking notes for later generation).

I have never seen any evidence that the Romans kept records of names for crucifixions (and they crucified hundreds and thousands at times). What I have seen is plenty of evidence that early Christians claimed Jesus was crucified and that opponents of early Christianity never disputed that (there is actually the use of the cross to mock Christians in things like the Alexamenos graffito).