The Irish form of Clara, stemming from a Latin word meaning “radiant, light.” So if you don’t mind raising a little girl who always wants to be center stage, Clare is a great choice.
There's pretty much no shortening Clare.
Famous people named Clare:
Author Clare Booth Luce; artist Clare Leighton; fashion designer Clare Potter; singers Clare Torry and Clare Burson.
Perhaps someday your little Clare will grow up and visit County Clare, Ireland.