Why are the rare earths erbium (Er), terbium (Tb), yttrium (Y) and ytterbium (Yb) named like that?
The links provided below are to the website "Elementymology &amp; Elements
  Multidict".  It is a fascinating site with information on the
  discovery, naming and various other facts for each element. As the author (Peter van der Krogt) says, "I am not a chemist, but a (map) historian much interested in the origin of names". Enjoy!


A nice piece on the complex etymology for Erbium, Terbium and Yttrium can be found here.  In brief the article says, "All three names were derived from the Ytterby quarry where the gadolinite was originally found in 1787. It is also said that since the original earth was divided into three new earths, Mosander split the name of Ytterby in three parts: ytt, terb, and erb."

As to ytterbium's etymology see here.   Again the history is complex with the name changing as recently as 1925. Another chemist isolated this element and again, wanted to pay homage to the geographic point of discovery, the Ytterby quarry.