The OFFICIAL name, which it was given by Congress in 1877, was as follows "War Between the States"....so take your "rebellion" and........(well, you'll think of something I'm sure!)
That's odd, considering that the title given to the War Department compilation of the records of the war was called "The Official Record of the War of the Rebellion" and it wasn't published until 1880. Sure you don't want to double check that claim?