House of figs or house of affliction
A modern phonetic spelling of the biblical place name Bethany. In the New Testament, Bethany was a village near Jerusalem where Lazarus and his sisters Mary and Martha lived.
Less common today
Bethanee isn't in the latest US Top 1000. It last peaked at #6,978 in 1994.
US births per 5-year period, 1990βpresent (SSA data).