The Zhuangzi often makes reference to fame as the enemy of the sage, but seldom (it seems to me) in a way that makes it immediately clear why this is so. Take for an example its reference in the introductory passage of Chapter three: "In the making of 'good' there-should-be-no going near name and fame. . . ." (Wu) We are often given examples of how name and fame (which are more or less equivalent) frequently lead to some form of persecution. This parallels a similar negative consequence of "usefulness"; draw attention to yourself, and someone will want to make use of you. The bark of the cinnamon tree is tasty, so we take it and kill the tree. Politically, if you rise above others, someone will surely wish to bring you down. These might be described as external punishments for fame. But though this is an important consideration in the Zhuangzi, possibly revealing a deep affinity for the philosophy of Yang Chu (who, according to his detractors, "would not give a single hair from his body to save the world"), it is not, I think, its most important dimension. That would be in the internal consequences of having a 'name'.
"The sage," we are told, "has no name." This has more to do with her own self-awareness, than it does with how others perceive her. She is not "somebody" to herself. She is empty. Because the world does not revolve around her, she is able to embrace all the world and each of its 'things'. This is the heart of her sagacity. This is her freedom.
Name (reputation, fame), when grasped as a value, renders impossible transcendence of egoic self-absorption. "For every name, we think, there turns out to be a substantial reality, so we take ourselves too as some kind of palpable material." (Chap. 23; Ziporyn) Name is that which helps establish us as 'someone' when the Daoist goal is to be no one.
"Who can free himself from achievement and fame / Descend and be lost amid the masses of men? / He shall be like Dao, unseen. / He shall go about like Life itself, with no name and no home." (Merton; The Way of Chuang Tzu; misquoted from memory)
Perhaps the most significant aspect of this insight is not the presentation of an ideal goal, but the realization of how this hunger for name is always with us and then working with it. It is unlikely that I, at least, could ever realize the ideal. This being the case, the true value of engaging in the Daoist sense of spirituality is in the engagement itself. If the process is not itself sufficient in itself, then the whole project is senseless. Goal-bound living is not philosophical Daoism; goals there are, but it is the living that counts; always we are affirmed where we are, as we are; the journey is all.
You can check out Scott's writings on Zhuangzi here.