This is the name of a place. (See: [[rc://en/ta/man/translate/translate-names]])
# to carry along the memory of my name
Absalom uses the phrase "my name" to refer to himself and his family line. AT: "to carry on my family name, by which people would remember me" (See: [[rc://en/ta/man/translate/figs-metonymy]])
# so it is called Absalom's Monument to this very day
This can be stated in active form. AT: "so people called it Absalom's Monument from that day on" (See: [[rc://en/ta/man/translate/figs-activepassive]])
# to this very day
This refers to the present time when this book of the Bible was written.