Douglas Harper's Etymology Dictionary
pack-rat
common name for the North American bushytailed woodrat (Neotoma cinerea) 1885, from pack (v.); so called from the rodents' habit of dragging objects off to their holes. Used figuratively or allusively from c.1850 of persons who won't discard anything, which means either the rat's name is older than the record or the human sense is the original one.
Wiktionary
pack-rat
n. (alternative spelling of pack rat English)