The name Hepzibah is a girl's name of Hebrew origin meaning "my delight is in her". Hepzibah and is often added to lists like Bible Names for Girls and discussed in our forums with posts like "Picky Parents - Sibsets Version".
From the experts:
This is a streamlined spelling of the biblical Hephzibah. Hephzibah is an Old Testament name that came into use in the 17th century, but is not often used today. It does have less formal nicknames Eppie and Hepsie, which seem revivable. Hephzibah "Eppie" Cass/Marner is the heroine of George Eliot's novel Silas Marner and Hepzibah Smith is a witch in the Harry Potter series.