What is carbon's scientific name?

You have answered your own question....the (English) scientific name of the atom that has 6 Protons and 6 Neutrons IS Carbon...

If you're looking for the archaic nomenclature then, oddly, this was one of the first elements formally named...prior to the formal naming, it was called "coal" or "soot".

Unlike things like Saltpeter (potassium nitrate) and Aqua Regia (Nitric Acid, Hydrochloric Acid)...carbon has been, and continues to be, a staple of modern and archaic chemistry.