John Gill Commentary 1 Kings 9:3

"And Jehovah said unto him, I have heard thy prayer and thy supplication, that thou hast made before me: I have hallowed this house, which thou hast built, to put my name there for ever; and mine eyes and my heart shall be there perpetually." — 1 Kings 9:3 (ASV)

And the Lord said to him, I have heard your prayer and your
supplication that you have made before me
With delight and pleasure, and had accepted it; meaning the prayer recorded in the preceding chapter:

I have hallowed this house which you have built ;
by the cloud of glory filling it, and by fire descending from heaven, and consuming the sacrifices offered in it, (2 Chronicles 7:1)

to put my name there for ever ;
there to grant his presence, so long as his pure worship continued in it; so the Targum adds, "and my Shechinah or divine Majesty shall abide in it, if my will is done there continually:"

and my eyes and my heart shall be there perpetually ;
his eyes of Providence should be upon it, to watch over it, and protect it, and its worshippers; and he should have a cordial regard to the sacrifices there offered, and to the persons of the offerers, so long as they offered them in a right way, and to right ends and purposes.