There is only one passing phrase discussing, directly, the relativity of fame:
For greatness is not absolute; comparison increases it or lessens it. A ship which looms large in the river seems tiny when on the ocean. A rudder which is large for one vessel, is small for another.
It is a good reminder, whether addressing the topic of fame, skill, riches, health or any number of indifferents, to remember that they are all mostly relative. If you think you possess a bit of an indifferent, the odds are overwhelming that someone has more than you and someone has less than you. The reason why you should keep this thought in your head is so that you are reminded that whatever it is you have, doesn't really mean anything; rather it just is. No need to get all worked up that you have less than someone else an no need to be anxious that you don't have more than someone else.
Spend your time and concern and care on your soul. To be clear, you do need to interact and use indifferents wisely. But they should not be your primary concern. Provide food, shelter, clothing, education and so forth for yourself and your family. But do so wisely; not extravagantly nor sloppily.
As for fame - focus on being an influence for good in your circle. If your circle continues to widen (more fame and influence), use it wisely. This is where much of modern society flounders, as many use their fame for petty, ignorant and useless things.
The last part of the letter is somewhat related to fame (being seen or not), but deals more with judging a person's character and where a person's feels guilty or not by allowing others to peer into his life.
I shall mention a fact by which you may weigh the worth of a man's character: you will scarcely find anyone who can live with his door wide open. It is our conscience, not our pride, that has put doorkeepers at our doors; we live in such a fashion that being suddenly disclosed to view is equivalent to being caught in the act. What profits it, however, to hide ourselves away, and to avoid the eyes and ears of men? A good conscience welcomes the crowd, but a bad conscience, even in solitude, is disturbed and troubled. If your deeds are honourable, let everybody know them; if base, what matters it that no one knows them, as long as you yourself know them? How wretched you are if you despise such a witness!
The spirit of this last part seems to be saying: let others see your life; if your actions are noble, then no need to hide behind closed doors. But if your actions are foolish, it doesn't matter that others see them, only that you recognize them yourself and are willing to submit to correction.