There's a poem by
Edith Sitwell that begins '
Daisy and
Lily, lazy and silly' so perhaps you might reconsider
Lily.
I assume that you're writing a story. When is it set? And where? Unless it's on a different planet or something, you could look up the popularity lists for the approximate decade, find
Daisy and then look at the names on either side of it until something seems to fit.
Otherwise, if you could give us more information it would help.