There was no one by the name Tom Bigbee, it seems.

source

The name “Tombigbee” comes from Choctaw “itumbi ikbi“, which means “box maker” or “coffin maker”. There are many stories and legends about how this name came to be. One story is the river was named after a box maker who lived on some of the Tombigbee’s headwaters. Another story is based on the need for box making in the area to ship pelts during the French-dominated fur trade in the 1700’s.

Umm... Choctaw

are a Native American people originally based in the Southeastern Woodlands, in what is now Mississippi and Alabama.