their abominable idols

"their idols which I hate"

the house that is called by my name

Here "name" represents Yahweh. This can be translated in active form. Alternate translation: "the house that belongs to me" or "the building in which they worship me" (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-metonymy)