What is the name of the underground city beneath Arkham City?

The underground city beneath Arkham City is called Wonder City.

Wonder City is an ancient subterranean settlement connected to Ra's al Ghul and the League of Assassins. Batman reaches it while following one of Ra's assassins through the ruins beneath Old Gotham, during his search for blood that can help cure the illness caused by the Joker's Titan-infected blood.

The ruined city is more than a hidden location: it reveals part of Ra's history and his obsession with Lazarus Pits, which can restore or prolong life. Its architecture and ceremonial spaces give the League a mysterious historical backdrop beneath the modern prison complex.

A common mix-up is confusing Wonder City with Wonder Tower. Wonder Tower is Hugo Strange's prominent headquarters and the launch point for Protocol 10, while Wonder City is the buried ancient settlement below Arkham City. “Old Gotham” refers to the ruined district above and around the underground site, not the city's proper name.