From reddit u/rforqs:
"Damhán" is a diminutive of "damh" meaning "ox" and it might come from Proto-Indo-European "dṓm" meaning "house" or by extension "domesticated" and many Indo-European languages use this root to refer to animals that work for humans or tend to be found near them (example "house cat", "house fly"). Now "Alla" has many meanings, but one definition roughly means "wild" or "crazy" (it can also mean "undomesticated" but don't worry about that). So it would make sense that the word's "literal translation" is something like "crazy house (creature)". Of course this compound word likely formed many centuries ago so that even if the components still exist today, the logic behind it is lost to time (you try telling me why call them ladybirds/ladybugs, or how a chesterfield could refer to a sofa).
Wiktionary says that damh comes from Proto-Indo-European dm̥h₂-ó- (“bull”), not dṓm. damhán alla is not restricted to house spiders.
As for ladybird, see https://forum.duolingo.com/comment/4291158?comment_id=29055461, and according to Wikipedia, "The first leather chesterfield sofa, with its distinctive deep buttoned, quilted leather upholstery and lower seat base, was commissioned by Philip Stanhope, 4th Earl of Chesterfield (1694–1773)."