Xiang Yu is known as the overlord of Chu, so what is Liu Bang's name?

After the founding of the People's Republic of China, Liu Bang's country name was Han. So far, we all call him Han because Liu Bang was once called "King of Hanzhong", which means three words. After capturing Xianyang and destroying Qin, heroes of all walks of life have titles. Xiang Yu claims to be the overlord of Chu, and Liu Bang's territory is Hanzhong, so Liu Bang's country name is "King of Hanzhong"