What does Leviathan mean?
Hebrew livyathan, a great sea-serpent/monster, generally glossed 'twisted, coiled' and derived (per Gesenius) from the root l-w-h 'to twine, wind' with a suffix, i.e. 'wreathed one'. Flag: the derivation is disputed (some hold it a loanword), and in use it is the name of a biblical serpent-monster; the 'coiled serpent' sense is the established reading.
What does Zion mean?
From Hebrew 'Tziyyon', the name of a hill in Jerusalem that came to stand for the city, the Promised Land and a place of peace. A long-standing biblical/geographic name now popular as a given name.