According to Wikipedia cowslip is an old country word for cow dung (and there was I thinking it related to the other end of the animal) and was applied to the flower because of its liking for muck. Other common names- still according to Wikipedia- are cuy lippe, herb peter, paigle, peggle, key flower, key of heaven, fairy cups, petty mulleins, crewel, buckles, palsywort, and plumrocks. Common? I've never come across any of them before. Most of them are prettier or quainter than cowslip- but I don't suppose there's any way people can be persuaded to start talking about herb peter or crewel. Names stick. Besides cowslip is in Shakespeare.
The botanical name is primula veris.