I'm not sure of the actual name of this wood, we call it 'badger wood' as it has loads of burrows.
Speaking of folklore though, holly is pretty important. In pagan mythology it is symbol of the Holly King, who rules between mid-summer solstice and and the mid-winter solstice. He represents the dwindling cycle of vegetation in this time.
Gifts of holly wreaths have been given between friends to celebrate winter solstice since Roman times.
Holly is also important in Christian tradition, it became symbolic of Jesus' crown of thorns.