Another story is that during the reign of Queen Victoria, one of the Wild West Rodeo - type shows came over to England. The owner of this show made a present to Queen Victoria of a red indian girl who was a part of this act.
Queen VIctoria was apparently too polite to refuse this "gift" but needed somewhere to house the girl, far from the possibility of embarrassment. The Duchy of Cornwall apparently had land and properties at or near Indian Queens; whither she was sent to be looked after.
Hence the place becoming known as The Indian Queen. Which may have become corrupted by usage (and the Ordnance Survey) into Indian Queens.