The name occurred rather late in the scheme of things. There was a great popularity in naming things after the Moors, mimicking them and making fun of them,... once they were made to leave Europe of course.
During certain times of year, in Old and Ancient England, the peasants would put on pageants that mocked the land holders, the local officials and anyone else that usually they weren't allowed to contradict. They would also make pageants about current events and heroic fantasy,... (such as fighting off the Moors)
One tradition was the Mummers plays, where the dancers would come to the landholder's house (local lord), Morris dance, sometimes do a pageant and have dinner at the lord's table all without speaking and usually in blackface (though customs in different villages and counties differ.)

Most often the items used in Morris dance were kept in parish church. The dances were outlawed under various religious leaders- Cromwell, for instance. And the horn dances in particular, were strictly outlawed when the peasants lost their hunting rights. (Only the landholders were allowed to hunt deer).
The dances almost did die out. They were resurrected by Cecil Sharp, who's passion was folk music and dances. He traveled to different villages and talked to the old men,.. some of whom only remembered seeing the dances as children. They taught him what they could and it became an academic pursuit for a good while.
This is one reason why so many times the dances are done without the energy and passion that a fertility rite would inspire. Old men taught them to scholars. Academia is not known for it's dancing passion.

Fertility... It is said that the hand-kerchiefs are representative of the head of the grain. So the higher one jumps the higher will grow the grain. It is also said that it represents sperm. The bells awaken the spirit of the land, and scare off any evil. The sticks, the same.