Cleopatra's needle(s) are obelisks originally built by Thutmose
III in 1450 BC. and they praised his achievements. Later Ramses II
added his own praise for himself to them. You could say they were
ancient brag books about two Pharaohs and had nothing at all to do
with Cleopatra. "Cleopatra's Needles" is just an exotic name that
someone made up for the obelisks.