A quick review of Mary Chestnut's diary, Sarah Morgan's diary, Jones "Rebel War Clerk's Diary," William Baclay Napton's Journals, Douglas's "I rode with Stonewall" and Pollard's 1866 "The Lost Cause" show that at least those Southerners referred to it as assassination or murder.
"Assassination" was used because that is what it was - the killing of a public figure for political reasons, just as the term was used for the killing of Czar Alexander, James Garfield, William McKinley, the Archduke Ferdinand, JFK, etc...