There is no clear cut list of Civil War Soldiers, I don’t think there will ever be.
Here are a collection of books that name Confederate or Union Soldiers either by State or that are buried in National Cemeteries.
The search engine on this site is pretty good at pulling data from PDF files if your have a name.
Confederate Soldiers buried in Chicago Illinois
Confederate Soldiers buried in Richmond Virginia
Groton Massachusetts Roll of Honor
List of the Immortals 600 Confederate Officers taken Prisoner
State of Connecticut
Union Soldiers buried in Nashville Tennessee
Union Soldiers buried in National Cemeteries in Missouri Mississippi and Tennessee
Union Soldiers buried in National Cemeteries Mississippi and Indiana
Union Soldiers buried in Texas
Union Soldiers of Champaign County, Ohio
Wisconsin Losses in the Civil War