Erbium is named after the swedish find spot Ytterby, just like Yttrium, Terbium and Ytterbium. Apparently the chemists of that time were not very creative in naming.
Therefore Erby is the third monster of the Ytterbies.
The name Holmium is derived from the Latin version of the city of Stockholm, because the element was discovered in Sweden. Therefore the moster design is inspired by the coat of arms of Stockholm:
The element samarium was named after the mineral samarskit, which in return was named after the russian mining engineer Vassili Samarsky-Bykhovets, whom almost nobody remembers nowadays.
Promethium was named after Prometheus, one of the titans of greek mythology, who brought fire to mankind. The gods then punished him by binding him to a rock in the Caucasus. There an eagle came every day eating his liver, which always grew back.
The name was chosen as a warning to humankind, since this element is radioactive as a product of decay of uranium. By the time of the discovery the nuclear arms race between the USA and the Sovied Union had begun.
The name means something like "green twin". When scientists discovered it, they called it didym. Later it turned out, that it consists of two very similar elements: praseodymium and neodymium.
The name is derived from an Ancient Greek word meanin "to lie hidden", because it was hard to find and isolate this element. It is the eponym of a whole group of elements: the lanthanides.