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I talked to my professor again (she is from Germany), and she said that in the German language, "an" means "at," "der" means "the," and "eck" (which she thinks must be the "egg" in our name) means "corner." So, apparently, "at the corner" is a pretty direct translation of "anderegg." Apparently, the spelling "andereck" is in the same Soundex category as "anderegg," which makes me think that maybe the meaning of the names is the same. I don't know for sure -- just a guess.
This is all I know about my husband's ancestry: he is Gaines Allen Anderegg Jr. (b. 7/12/68 in Charlottesville, VA); father: Gaines Allen Anderegg Sr. (b. 11/13/44 in Nashville, TN); grandfather: Phillip Lemuel(?) Anderegg (b. 1920 (?) in TN); great-grandfather: John(?) Anderegg (died in the 1940's). He doesn't remember anybody before that. We will keep looking, though.