en_tn/2sa/18/18.md

the King's Valley

This is the name of a place. (See: rc://en/ta/man/jit/translate-names)

to carry along the memory of my name

Absalom uses the phrase "my name" to refer to himself and his family line. Alternate translation: "to carry on my family name, by which people would remember me" (See: rc://en/ta/man/jit/figs-metonymy)

so it is called Absalom's Monument to this very day

This can be stated in active form. Alternate translation: "so people called it Absalom's Monument from that day on" (See: rc://en/ta/man/jit/figs-activepassive)

to this very day

This refers to the present time when this book of the Bible was written.