|Well, that's not its name ... but ...
The term "Resistance against Fire Lord Zuko" has not been confirmed by official sources.
|"You and I have longed for the glory days of Ozai's rule, when the Fire Nation was the strongest and safest of all the nations! No outside threat stood a chance against us! Little did we know that we would be undone from within by Zuko, our own crown prince! Believers like us had to go underground. We worked long and hard, preparing for the day when we could finally remove that impostor!"|
|— Ukano to the New Ozai Society.|
In his early reign, Fire Lord Zuko faced significant resistance from Fire Nationals who regarded his rule as illegitimate and his policies as treason against the Fire Nation. His main opponents were nationalists and reactionaries, many of whom were Ozai loyalists, and Fire Nation colonists who wanted to maintain their homes in the face of the Harmony Restoration Movement. These resistance movements were exploited by the rogue princess Azula who worked to turn Zuko into an autocrat.
From the reign of Fire Lord Zoryu, the Fire Nation developed into an increasingly effective autocracy. Exploiting this political power as well as the Fire Nation's economic and military might, Fire Lord Sozin launched the Hundred Year War to conquer the world. Under his rule and that of his son Azulon as well as grandson Ozai, the Fire Nation was turned into a imperialistic dictatorship whose people were indoctrinated with propaganda. Fire Nation citizens were taught that their civilization was superior and their country's wars of conquest brought order and progress. Many colonies were set up in the Earth Kingdom, and the Fire Nation successfully conquered most of the world.
Before the Fire Nation's final victory, the country was defeated thanks to the intervention of Team Avatar which included Zuko, the Fire Nation's crown prince who had turned against his father Ozai. While Ozai was imprisoned for numerous war crimes, Zuko was crowned new Fire Lord. He set out to reform the Fire Nation as well as restore a cooperative and peaceful world order.  To do so, he pledged to support the Harmony Restoration Movement which aimed at dissolving the Fire Nation colonies.
Buildup of an underground opposition and assassination attempts
In the immediate aftermath of Zuko's ascension to the throne, Ozai's loyalists were purged from the government or voluntarily went into opposition. Some organized into militant underground movements, the most important of which was Ukano's New Ozai Society. Unrest also grew in the older Fire Nation colonies whose ethnically mixed population strongly opposed being removed from their homes. Many colonists such as Mayor Morishita of Yu Dao regarded Zuko as traitor for betraying the colonies to the Earth Kingdom.
In the first months of his rule, there were five assassination attempts targeting Zuko who survived all of them unharmed. However, he became paranoid and distrustful of his bodyguards' capabilities. To increase his personal security, his followers convinced the Fire Lord to move into an especially fortified tower of the Fire Nation Royal Palace. Regardless, a Fire Nation colonist named Kori Morishita managed to get past all defenses and tried to kill Zuko. Despite failing to assassinate the Fire Lord, Kori's action ultimately contributed to the Harmony Restoration Movement's failure and the retention of the oldest colonies.
In addition, the failure of his bodyguards led Mai to request the Kyoshi Warriors to act as Zuko's personal security after Kori's assassination attempt. While they proved to be more capable than the old security, the employment of foreigners as his guards further alienated Zuko from Fire Nation nationalists.
Rebellion of the New Ozai Society
While Zuko was mostly concerned with the Harmony Restoration Movement and then the search for his long-lost monther Ursa, spending months away from the Fire Nation Capital, Ukano's rebel group continued to grow. However, his attempt to enlist Mai in the New Ozai Society resulted in complete failure. Despite not reporting him to the autorithies, Mai consequently began to monitor the New Ozai Society's activities, hoping to intervene if they ever became a threat to Zuko. In this, she was aided by Kei Lo who acted as her mole in the underground movement.
As Ukano was preparing a major uprising, he was eventually contacted by Azula and her followers, disguied as Kemurikage spirits. The rogue princess implored Ukano to speed up his uprising plans, appealing to his nationalism as well as threatening to harm his family if he refused. Utterly frightened, Ukano decided to follow this order despite knowing that the New Ozai Society was probably too weak yet. Unbeknowst to him, Azula was actually using him as a mere pawn; she wanted to keep Zuko in power, and only intended to use the Ozai loyalists to influence her brother's governing style.
Around 102 AG, the New Ozai Society prepared to strike, planning to kill Zuko as he was returning with Ursa to the Fire Nation Capital. Having identified Kei Lo as mole, Ukano told him false plans so that he would transmit them to Mai as well as the Fire Lord, thereby luring his enemies into an ambush. As the rebels hoped, their opponents fell for their trap. The Fire Lord and his allies set up a decoy convoy that was dispatched along the official route from the First Lord's Harbour to the palace. This convoy was attacked by a small diversionary group of New Ozai Society militants who were easily defeated by Fire Army soldiers, Kyoshi Warriors, and Mai. At the same time, the rebels' main force assaulted Zuko's actual caravan in the woods near the capital, and almost suceeded in killing him as well as his family. However, the Fire Lord and Kei Lo held Ukano's followers off long enough for reinforcements to arrive with a hot air balloon. Thus bolstered, the Fire Lord'a allies defeated and captured most of the New Ozai Society. Ukano managed to escape.
After the failure of Ukano's uprising, Azula kidnapped children in the Fire Nation Capital. By using their Kemurikage disguise, Azula's followers made it appear as if the spirits were angry at Zuko's rule, thereby undermining the population's support for him. To exploit this, Ukano set up the Safe Nation Society that publicly claimed to protect the citizens from dark spirits. In truth, it acted as conduit for Ukano to spread his nationalist and reactionary ideology. Before the Safe Nation Society could gain enough momentum to actually threaten Zuko's government, however, Azula instructed Ukano to organize a riot in the capital. Despite his misgivings, Ukano obeyed. Just as the princess had hoped, the riot resulted in the destruction of the Safe Nation Society while furthering Zuko's trend toward authoritarianism. He organized a curfew, mass arrests, and used the Fire Army to keep the population under control. Azula believed this kind of governance to be ideal.
Before Zuko descended into tyranny, however, Avatar Aang and his other allies discovered Azula's hideout in the Garden of Tranquil Souls. There, Zuko's forces freed the kidnapped children with Ukano's help who had begun to question his allegiances. Azula also revealed to Zuko that she intended to become the power behind the throne, aiding Zuko by turning him into an autocract. Despite him rejecting her vision for the Fire Nation, the princess maintained her stance before disappearing alongside her companions. Later on, Zuko publicly apologized for his aggressive policies during the Kemurikage crisis, promising to do better in the future.
The opposition movement against Zuko ultimately failed to remove him as Fire Lord, although it influenced some of his decisions and policies. The failure of the Harmony Restoration Movement ultimately led to the formation of the United Republic of Nations. Overall, Zuko steered the Fire Nation away from its imperialist past, restoring its reputation throughout the world and greatly helping to maintain peace. The nation and its people began to work to redefine themselves away from the terrible crimes of their past, without losing their traditions, heritage, and thirst for innovation.
Zuko remained in power until he stepped down from his position in 167 AG, passing the throne to his daughter Izumi. She maintained her father's disdain for the Fire Nation's imperialist and expansionist past.