It means 'horse tamer' from hippos, 'horse' and damao, 'to tame', and as a favourable name really means 'one who is high-born', 'one who owns many horses'. (Significantly, even today, in a different era and a different culture, the prestige of owning and riding a horse is still considerable, not least for a woman.) One should not overlook the 'taming' aspect of the name, either, which relates to the mastery of horses and chariots. (A goddess so named could give a person the power to tame horses.)
There is a specific connection for Hippodamia the wife of Pelops, since she married her husband as the result of a 'rigged' chariot race which he won - and thus qualified to carry her off. Jane Harrison sees this story evolving from actual races which took place in the original Olympic games; in these, young men raced in chariots and girls (virgins) raced on foot.
