This is from
http://www.behindthename.com; everything I've always been taught confirms it.
REBECCA f
Usage: English, Italian, Biblical
Pronounced: re-BEK-a
From the Hebrew name Ribqah, possibly meaning "a snare" in Hebrew, or perhaps derived from an Aramaic name. This was the name of the wife of Isaac and the mother of Esau and Jacob in the Old Testament.
I always though Isaac seeing Rebekkah first by the well to be particularly nice

ANNE f
Usage: French, English, German, Scandinavian, Finnish
Pronounced: AN
French form of HANNAH. This is the name traditionally assigned to the mother of the Virgin Mary, though she is not mentioned in the Bible. The name was borne by a 17th-century English queen and also by the second wife of Henry VIII, Anne Boleyn (the mother of Queen Elizabeth I), who was eventually beheaded in the Tower of London. This is also the name of the heroine in 'Anne of Green Gables' by Canadian author L. M. Montgomery.
HANNAH f (Hannah does not appear in my name but Anne is a version of Hannah so I included it)
Usage: English, Jewish, French, Biblical
Pronounced: HAN-a
From the Hebrew name Channah which meant "favour" or "grace". Hannah was the mother of Samuel the prophet in the Old Testament. The Latin version of this name is Anna.
Therefore Anne really means favor or grace. Although my name is spelled Ann, not Anne (though I infuriated my father enough after reading Anne of Green Gables by spelling it that way

)
My last name, which obviously can't be said here, starts with a G and is Dutch, not Irish in origin. (One of my brothers looks very Dutch, actually.)
So my initials spell RAG

<poof!>
Rune
P.S. in the case of my forum name I usually go on the web by Rune of Westhaven, which is a name from a series of books by Mercedes Lackey, Bardic Voices.