I like the idea of
Cosette because of its literary and theatrical ties, but Cozy I think is on par with something like
Princess or
Precious or Lamb - ok as a family name, but not for everyday use. It's way too cutesy. I like the zappier, stronger Zettie or Zette.
I'd pair
Cosette with something more serious and mature, like
Cosette MiriamCosette LucilleCosette Agatha,
Cosette Agnes (though they sound nicer as
Agatha Cosette and
Agnes Cosette imo)
Cosette MarthaCosette BlancheCosette FredericaCosette BarbaraCosette HenriettaCosette MarjorieCosette RebeccaRose Cosette