The university of Leipzig in Germany has a "Namensberatungsstelle", something like a information center for
German given names. It is known as an authority in this matter. They list
Doris on one of their name info pages:
http://www.uni-leipzig.de/~vornam/wcms/index.php?option=com_content&view=article&id=29&Itemid=35
They say there that
Doris became popular during the "Rokoko" (Late Baroque, 18th century) together with some other names in the wake of a type of literature called "Schäferpoesie" in
German. Here an entry in a
German encyclopedia from 1857 about that literary movement:
http://www.zeno.org/Herder-1854/A/Schäferpoesie
I couldn't find an English translation for "Schäferpoesie"; maybe "pastoral poetry"?