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/translate/figs-metonymy]])
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/translate/figs-activepassive]])