There are no passenger rail trains that travel directly from Atlanta to Miami, but Amtrak does offer indirect routes between the cities.
Passengers will have to travel from Atlanta to another city first, then transfer to another train before continuing on to Miami.
Amtrak generally routes its service between Atlanta and Miami through Union Station in Washington D.C. Other transfer points are Charlotte and Raleigh, NC.
The name of the Amtrak train you would take out of Atlanta is the "Crescent," transferring to the "Silver Star" in Washington D.C. or the "Carolinian" in Charlotte and then transferring to the "Silver Star" in Raleigh. The "Silver Star" will then take you to Miami.
There are no other passenger rail companies that provide service between Atlanta and Miami.