Why does the 1st Battle of Bull Run / Manassas have two names?

the first of two engagements fought at a small stream named Bull Run, near Manassas in northern Virginia.

Explanation:

Civil War battles often had one name in the North, which was usually associated with a prominent nearby physical feature, and another in the South, which was usually derived from the town or city closest to the battlefield.

So, where Northerners saw Bull Run, a tributary to the Occoquan River, Southerners thought about the local railroad station nearby in Manassas, Virginia. It was also convenient to their final resting places. So, now the battle had two names ... With a few notable exceptions, the battles were named by the victor.