All the older characters want in Daisy Miller is a little R-E-S-P-E-C-T. But that don't mean much to D-A-I-S-Y. She's more Cyndi than Aretha. In fact, Daisy and Mrs. Costello represent two theories of how you ought to live.
In the Mrs. Costello school of thought, one must always be aware of how what one does reflects on one, and also one must refer to oneself and others as "one" all of the time because one has a pretty clear idea about how any and every one must behave. In the Daisy school of thought, you only live once, so ignore the haters and do whatcha wanna. It sounds like Daisy's school is a lot better. But don't forget that she dies in the end from all of that fun—so we can't be too quick to jump to conclusions.
Between Mrs. Costello's sad life and Daisy's sad death, James seems to be saying that the tightrope of reputation must be carefully crossed. That is to say, don't let what others think of you dictate your every move, but don't forget to wear underwear while exiting a limo, either.
Daisy intentionally creates a sense of notoriety for herself because it is a more powerful status than respectability.
Winterbourne's reputation is solely based on his social and familial associations. There is nothing in his behavior or personality that generates a reputation of his own.