Dammsugare is ’vacuum cleaner’ or ’hoover’. Damm is ‘dust’, earlier damm has also meant ‘vapour, ‘steam’, the English relative is damp. Both the Swedish and the English words probably derive from German Dampf, ‘vapour, Germanic *dampaz.
English dust derives from Germanic *dunstaz, German Dunst, from which comes Swedish dunst, meaning just ‘vapour’, ‘fume’. Further back is the Indoeuropean root *dheu-, also leading to Latin fumus, ‘smoke’.
Att suga is ‘to suck’, both go back to an Indoeuropean root *sug- with the same meaning.
Hoover is a trademark for a vacuum cleaner, that is also used generally for ‘vacuum cleaner’, also as a verb to hoover = ‘to vacuum’. Swedes often mix up hoover with hover ‘soar’, ‘hang suspended in air’ which is what helicopters and hummingbirds do (Swedish = ‘sväva’, ‘kretsa’).