Ariel was the name of a man contemporary with Ezra. This is also one of Jerusalem’s appellations, as attested in the verse: “Woe to Ariel, to Ariel, the city where David dwelt.” Isaiah 29, 1.
Eden is the place where God planted a garden for Adam and Eve; this is also the name of a Levite of the time of Hezekiah, king of Judah; this is also one of the names given to Jerusalem.
"Zion" is another name for Jerusalem and Israel. Its origin is found in Jerusalem's name prior to its occupation by King David: "Nevertheless David took the strong hold of Zion, the same is the city of David." 2 Samuel 5, 7