What is the real name of Lazio?

Could you please clarify for me, what is the actual, official, or commonly recognized name of the Italian football club Lazio? I'm curious to know if there's a name beyond the nickname or brand name that they're often referred to. Is it a name that's derived from the region they represent or perhaps has a historical significance? It would be helpful to have a clear understanding of the club's real name, if it differs from what's commonly used.