Chinese call themselves Tang People, here Tang is Tang Dynasty, one of two great dynasties in Chinese history. Tang is used as a surname only, almost no other meaning anymore.
Let's see what the original meaning of the character.
The shell bone script of character Tang is
The bronze script of character Tang is
The small script of character Tang is
The clerical script of the character is
which is changed very big. The top 厂 may be the character Working Site, the middle is character 聿, or 尹, both means "A hand holding a stick". The bottom is the gap.