Norah is the Irish form of Eleanor — itself ultimately from the Latin honor, meaning "honour," or the Greek helene, meaning "light" or "sun's ray." The H spelling is the older Irish form; Nora (without the H) is the simpler modern variant.
Norah has been continuously used in Ireland for centuries and in the U.S. for a hundred years. The American singer Norah Jones (born 1979) brought the H spelling renewed visibility. Today Norah sits in the U.S. top 100 and is climbing fast.
Norah reduces to seven — the number of quiet honour.