Henry James's novella Daisy Miller has often been compared/contrasted to F. Scott Fitzgerald's realist novel The Great Gatsby (see sidebar). It is perhaps in this comparison that one discovers several clues to the possible meanings of protagonist Daisy's name. Another interesting comparison is this title character to Maisie in James's What Maisie Knew.
Consider the billboard in The Great Gatsby and the "all-seeing eye of God" represented by the spectacles. If Daisy's name is derived from "Day's Eye" then this character sees and understands more than her antagonist Winterbourne perceives - just as Maisie sees far more than her parents realize. Additionally, her name symbolizes the link to the natural world. The polarity between Daisy's name and Winterbourne's also parallels the differences between American and European culture and mores.
Not much has been written about Daisy's surname; however, consider the drone of the mill and the Daisy's droning on about American Society (see link below).
As you explore this question further, consider any emotional components to the name or any feelings her name elicits. And what is the life span of a daisy? Finally, be sure to examine carefully how the tropes outlined in this answer ultimately relate to the enduring questions Henry James raises in this novella as well as in his other seminal works.