I believe both sides call it the Siege of Vicksburg.
Simply by location
Ulysses Grant.
The Siege of Vicksburg was fought in the vicinity of Vicksburg, MS.
The address of the Vicksburg Transportation Museum is: 129 Hoxie Rd, Vicksburg, MS 39180-6340
There was no captain named Vicksburg in the civil war, so no person of that name could have been important to the union or anybody else. Perhaps you are thinking of the battle of Vicksburg, which was critical.
The Battle of Vicksburg is also called the Siege of Vicksburg
Jackson, Mississippi
I believe both sides call it the Siege of Vicksburg.
Simply by location
Vicksburg
Vicksburg.
A thoroughbred named Cincinnati although Grant owned several horses including one name Jeff Davis which he got during Vicksburg from a plantation that Jefferson Davis owned in Mississippi.
Ulysses Grant.
It was named in honor of General Ulysses S. Grant's victory at Vicksburg
Vicksburg
The Battle of Vicksburg gave the Union control of the Mississippi River.