That all people of the earth may know thy name, to fear thee - Solomon prays that the result of Yahweh’s hearing the prayers of pagans addressed toward the temple may be the general conversion of the world to the worship of Him. Compare Psalms 96:1-13; Psalms 98:1-9.
This house ... - literally, as in the margin. In Scripture, when God’s Name is said to be “called upon” persons or things, it seems to be meant that God is really present in them, upholding them and sanctifying them. This passage therefore means, that the pagan, when their prayers, directed toward the temple, are granted, will have a full assurance that God is present in the building in some very special way.