The name was written literally GU-EDIN (or GU-EDIN-NA) in cuneiform. Radau suggests that GU here means Akkadian mātu "flat land, field" and EDIN means bamātu "open country, plain". (He also relates it to Hebrew bamoth "high places".) In other words, the name literally meant "the open fields".
EDIN meaning "plain" is pretty standard (though it's usually equated with the borrowed Akkadian edinu "steppe"), but this is a meaning of GU I haven't seen before. Still, it makes more sense than the usual meaning of GU ("net").
Source: Radau's Early Babylonian History Down to the End of the Fourth Dynasty of Ur, page 86 onwards. The book is from 1900, so take it with many grains of salt, but I haven't found anything more recent specifically discussing the GU part of this name.