The hiragana spells it かごめ. Which translated flat out has no meaning whatsoever.
Due to the Hitomiko episode in Kanketsu-hen, people have been led to beleive she was named after the Children's game: Kagome, Kagome. But that's not true either. Takahashi-sensei never said that she was ever.
The closest meaning that her name comes up with is "woven basket", so we can take that to mean that Kagome means "woven bamboo pattern." Which is much nicer then the children's game any how.