The name Remus comes from mythology. Remus (and his brother) founded Rome and he was raised by wolves. The last name Lupin comes from the Latin word 'lupus' which means wolf.
Sirius is named after the constellation Sirius, which is also known as the dog star. Sirius' surname, Black, is pretty obvious because Sirius has the ability to turn into a large, black dog.
Merope Gaunt's first name comes from mythology. Merope was a nymph who was shamed for marrying a mortal, much like Merope Gaunt was shamed for being in love with a Muggle.
|Artist depiction of Merope Gaunt by VanishingShmink|
The name Aragog likely came from the words arachnid and and gog. The word arachnid, obviously, refers to a spider. The word gog, on the other hand, was the name of a legendary giant. When you combine those words, they perfectly describe Aragog, a legendary, giant spider.
The name Quirinus Quirrell is derived from Janus Quirinus, the Roman god with two faces.