Possible meanings are 1) God's name represents himself. AT: "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. AT: "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. AT: "I will watch and protect it forever" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-explicit]])
# if you walk before me as David your father walked
Here walking is a metaphor for living. Walking before God represents living in obedience to him. AT: "If you obey me as David your father did" (See: [[rc://en/ta/man/translate/figs-metaphor]])
# David your father
Solomon was one of David's sons.
# keeping my statutes and my decrees
"obeying my statutes and my decrees"
# I will establish the throne of your kingdom
Here the throne represents ruling. Establishing the throne of Solomon's kingdom represents causing Solomon to have descendants who will rule over Israel. AT: "I will make descendants of yours rule over your kingdom" (See: [[rc://en/ta/man/translate/figs-metonymy]])
# A descendant of yours will never fail to be ruler in Israel