thats a really hard question to answer because many battles probably arent recorded. but since the north won the slave war i am guessing north did.
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The South liked to name them after the nearest town. The North liked to name them after the nearest water-course - river, stream or creek.
North
The majority of the large scale Civil War battles where fought in Northern Virginia, between Washington DC and Richmond (The Capitol of the South).
The battle of Peters burg was one of the last battles of the Civil War. Neither the North or the South won.
The North and the South sometimes named their battles differently. The North tended to name them after the nearest river, and the South after the nearest town.