The United States and the Confederate States of America had different systems for naming their armies and battles. Usually, the North named its armies after rivers, and its battles after rivers or creeks (Where available). The South named its armies after states, and its battles after towns.

The Army of the Tennessee (river), was the Union army. While the Confederates fought in the Army of Tennessee.

North South

1st Bull Run 1st Manassas
Peninsula Campaign Seven Days Campaign
Mechanicsville Beaver Damn Creek
2nd Bull Run 2nd Manassas
Antietam Sharpsburg
Wilson's Creek Oak Hills
Pea Ridge Elkhorn Tavern
Stone's River Murfreesboro
Pittsburg Landing Shiloh
South Mountain Boonsboro
Fair Oaks Seven Pines
Ball's Bluff Leesburg
Ox Hill Chantilly
Sabine Cross Roads Mansfield
Opequon Winchester

Just a few examples of names both sides used.

Now "Gettysburg" both sides used, Fredericksburg was also named the same, as more battles were.

Well hope I helped out a bit,

Have a good morning,

Shawn Prouty