world wide, they have many names (and as gemini helped me out here, here are few names.)
The basic idea for HnH purposes would be to: repair your stored in selected (and/or marked with proper decal) cupboards, gear items. restock your food table (from properly decal'ed cb's) or maybe even the study desk. A tiny object, like a little nest, just a place where we could give those spirits offerings, to keep them happy. Usually invisible, but when action is performed (repair = sound of clinking of hammer, restock = visibly floating food item over to a table) and witnessed, we could enjoy a little house magic. if we kept spirits happy enough, perhaps they could also organize our storages (since little other actions can be imagined as of now, like we don't really need sweeping or cleaning.) by sorting contents of cubpoards.Europe & Scandinavia
Domovoy / Domowik (Slavic Europe): The traditional master of the house, usually envisioned as a small, bearded old man (sometimes covered in hair). He resides behind the stove or under the threshold. If respected with gifts of milk, bread, or salt, he guards the family and livestock; if angered by messy housekeeping or coarse language, he hides objects, makes walls knock, or pinches people in their sleep.
Tomte / Nisse (Scandinavia): A small creature featuring a long white beard and a conical red cap. Associated with the homestead and farmstead, the Tomte cleans, tends to horses, and protects the land. He demands a simple bowl of buttered porridge, particularly on Christmas Eve; forgetting the butter can incite destructive tantrums.
Brownie (Scotland & England): A small, solitary fairy that comes out at night to perform household chores like churning butter, sweeping, and threshing grain. They accept small treats like cream or honey, but offering them clothes as payment insults them, causing them to leave forever or turn into a mischievous Boggart.
Kobold / Heinzelmännchen (Germany): In German folklore, domestic Kobolde reside in homes and help with domestic labor. The Heinzelmännchen of Cologne are a famous regional variant—small house-elves who completed all tasks for local craftsmen while they slept until a curious woman trick-spilled peas on the floor to catch them, driving them away forever.
Trasgu (Northern Spain - Asturias & Cantabria): A small goblin who wears a red tunic and hat and has a hole through his left hand. He sneaks into homes at night to clean or rearrange furniture. If offended, he breaks dishes and causes mischief. Household owners historically tried to get rid of him by giving him impossible tasks, like picking up seeds through the hole in his hand.
Lutin (France): A hobgoblin-like spirit that can shape-shift (often into a white horse or small animal). A pleased Lutin takes care of livestock and polishes cookware; an annoyed one turns milk sour and tangles horse manes.
East & South Asia
Zao Shen / Zao Jun (China): The "Kitchen God" or "Stove Master." Rather than performing chores directly, he monitors the moral behavior of the household from his post near the stove. Every Lunar New Year, he ascends to Heaven to report the family's conduct to the Jade Emperor. Families smear sweet rice or honey on the mouth of his icon to bribe him into speaking sweet words (or sticking his jaws shut).
Zashiki-warashi (Japan): Child-like house spirits with bobbed hair that inhabit traditional Japanese homes (particularly in Iwate Prefecture). They are benevolent spirits whose presence brings great wealth and good fortune to a family. Though prone to minor pranks (like leaving footprint powder or making noise at night), driving one away brings immediate financial ruin to the household.
Enma-da (Myanmar / Burmese Folklore): A domestic guardian spirit (Nat) worshipped near the main pillar of a house. Offerings of coconut and bananas ensure harmony, prevent house fires, and guard against domestic misfortune.
The Americas & Indigenous Traditions
Duende (Iberian America / Mexico / Philippines): Derived from Spanish folklore (dueño de casa, owner of the house), Duendes are dwarf-like creatures living inside house walls or attics. Depending on the region, they either help children keep things clean or hide keys, misplace items, and cause noises in the night when annoyed.
Chaneque (Mesoamerica / Mexico): Guardians of nature and domestic boundaries from Nahuatl lore. Small, child-like entities with reversed feet, they wander near homes to play tricks on inhabitants, hide personal belongings, and occasionally lure people into confusion if not respected with food offerings.
An actual visual representation of the house spirit could be fun (and probably demanding code-wise), but not truly necessary. Just knowing we have a companion in house could liven up the day to day grind. Perhaps they could scold you audibly once in a while for being messy, comment or you stuffing your stomach till it nearly bursts, or warn you when your study desk is nearly empty. Could be really cool place for an AI driven spirit speech.