Here we go. From Slack's first book Carnivorous Plants page 119:
Henery Lyte, the botanist squire of Lytes Cary Manor in Somerset, may have been the originator of its English name, for he has the following to say in his New Herbal of 1578
"This herbe is of a very strange nature and marvelous: for although that the sonne do shine hoate, and a long time thereon, yet you shall finde it alwayes full of little droppes of water: and the hoater the sonne shineth upon this herbe, so muche the moystier it is, and the more bedewed, and for that cause it was calles Ros Solis in Latine, which is to say in Englishe, the Dewe of the Sonne, or Sonnedewe"