No. I actually had the same question. The county was named after Thomas Willis Cobb, who was a senator and state representative in Georgia in the 1800's.
Ty Cobb was a center fielder for the Detroit Tigers and the Philadelphia Athletics. He still holds the record for the highest career batting average and the most career steals of home.
Yes, Cobb was born in Narrows, Georgia, making him a native of America. He was not a Native American in the modern use of the term in that he was not an American Indian.