The meaning of each state's renaming is as follows
Virginia is renamed Grant. Ulysses Grant commanded the various Union armies which defeated Confederate General Robert E Lee's forces defending Richmond.
North Carolina is renamed Burnside. Ambrose Burnside captured the North Carolina coast in the early part of the war. Although he disgraced himself as commander of the Army of the Potomac, Burnside was a political survivor and repaired his reputation with major political leaders.
South Carolina is renamed Lincoln. "South Carolina must be punished" drove much of the Union's thinking during the war. What better way to punish South Carolina than rename it after the leader of the Union?
Georgia is renamed Sherman. William Sherman commanded the Union army in its march of destruction from Atlanta to Savannah.
Florida is renamed Pickens. Fort Pickens was one of the only forts on the southern mainland to never fall into rebel hands.
Alabama is renamed Farragut. Admiral David Farragut was a key player in seizing the Mississippi River. He is also well known for yelling "Damn the torpedoes, full speed ahead!" during the Battle of Mobile Bay.
Mississippi is renamed Knight. Newton Knight led the anti-Confederacy Jones County rebellion in Mississippi.
Tennessee is renamed Johnson. Andrew Johnson was the only senator from a Confederate state to stay loyal to the Union.
Arkansas is renamed Steele. General Frederick Steele captured much of Arkansas including its capital of Little Rock.
Louisiana is renamed Butler. Benjamin Butler was the military commander of occupied New Orleans and much hated by the upper class of Confederate citizens.
Texas is renamed Houston. Governor Sam Houston was forced out of office by Confederates because he refused to denounce his pro-Union beliefs.