老聃 Lǎo Dān is generally recognized as 老子 Lǎozĭ, legendary author of the 道德經 Dàodéjīng. Traditional scholars frequently describe Laozi as the founder of Daoism and Zhuangzi as having developed his ideas. However, there are reasons to doubt this. Although the legend of Lǎozĭ preceded Zhuangzi, as evidenced by his presence in Zhuangzi's book, there is no solid evidence of the Daodejing's being in existence until a generation or so later. The fact that Zhuangzi does not quote it suggests that to me that he was not familiar with it. In trying to figure out what exactly the figure of Lǎozĭ represented to Zhuangzi, therefore, we should probably be careful of relying too carefully on the Daodejing but should begin, instead, from the treatment of Laozi in the text of the Zhuangzi.
Indeed, the term daojia 道 家 (our “Daoism”) was not coined until over a century after Zhuangzi's death by the
Han Dynasty historian Sima Tan (165-110 B.C.E.). Xunzi talks about Laozi
and Zhuangzi, but he does not refer to them in a way that suggests he thinks of
them as constituting a distinct school. Indeed, he does not
even refer to them together. So, while we now may think of them as constituting a Daoist school, there is no reason to believe they thought of themselves that way. While Zhuangzi evidently was aware of someone named Laozi that he was responding to, he certainly felt the same and even more so about Confucius, whose name appears in 55 distinct episodes as opposed to Laozi's 15.
老聃 Lǎodān appears in 3:05, 5:03, 7:04, 10:01, 10:02, 10:03, 10:04, 10:05, 10:06, 10:07, and 17:04. He is also referred to as 老子 Lǎozĭ in 10:03 and 10:07.