The empire opposing the heroes in Final Fantasy XII is Archadia, formally the Archadian Empire.
Archadia invades and occupies the kingdom of Dalmasca before the main story begins. Its expansion brings the heroes into conflict with imperial forces, especially Vayne Solidor, the ambitious son of Emperor Gramis and the game’s principal antagonist. The party’s broader goal is tied to Dalmasca’s liberation and the struggle over the empire’s use of nethicite.
Archadia is one of two major powers in Ivalice. The other is the Rozarrian Empire, which is not the primary enemy and sometimes works with the resistance against Archadia. That political rivalry gives Final Fantasy XII a more complicated conflict than a simple heroes-versus-one-villain story.
The distractors belong to other Final Fantasy settings. Gestahl is the emperor of the Gestahlian Empire in Final Fantasy VI, Baron is the kingdom central to Final Fantasy IV, and Galbadia is the militaristic nation in Final Fantasy VIII. They are recognizable names, but only Archadia fits Final Fantasy XII’s central imperial conflict.