Possible meanings are 1) God's name represents himself. Alternate translation: "that I may be there forever" or 2) God's name represents Yahweh's reputation, and his name being there represents people worshiping him there. Alternate translation: "for people to worship me there forever" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here "My eyes" represents God's careful attention, and "my heart" represents his love. These being at his temple implies that he will protect his temple. Alternate translation: "I will watch and protect it forever" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-explicit]])