For shame! I thought you would know that Minas Ithil was "Tower of the Moon", and Minas Anor was "Tower of the Sun". While "Isildur" and "Anarion" contain the same root stems as "ithil" and "anor", they don't mean quite the same. For instance, IIRC, the root "isil" is also used in the Quenya word for "silver".
OK, time for me to geek out (I'm geekier when I'm tired...)
Osgiliath was the capital of Gondor, while Minas Anor and Minas Ithil were the homes of Anarion and Isildur, respectively. When Minas Ithil was conquered by Mordor and became the home of the Nazgul, it was renamed Minas Morgul (Tower of Sorcery). Because of this, Osgiliath was no longer protected from the East and became a regular victim of attack; the capital of Gondor was then moved to Minas Anor, and it was renamed Minas Tirith (Tower of Guard). Osgiliath was gradually depopulated by the continuing attacks, until it was a ghost town. One of Boromir's great feats (with his brother's help, of course) before embarking on the quest of the riddle was to defeat the forces of Mordor and free Osgiliath from their control, for a time.
I wuz jokin'. But still.
Nice recap! Didja do all that from memory?
I thtill think we thould call him Ithildur.