Taegukgi

In 2003, while digging up remains at a Korean War battlefield to set up a memorial site, a South Korean army excavation team notifies an elderly man that they identified some remains as his own, after finding his name on the active list, not on KIA or MIA lists.[N 1]
Decades earlier, in June 1950, in the South Korean capital of Seoul, the Lee family go about their lives. Jin-tae Lee owns a shoeshine stand to pay for his younger brother Jin-seok's education. Jin-tae also bought a silver pen for Jin-seok. Jin-tae's fiancÃ©e Young-shin works with the Lee's noodle shop. On June 25, 1950, North Korea invades South Korea. Both brothers are forcibly conscripted. They then become a part of the 1st Infantry Division, fighting at the Pusan Perimeter and then advancing north. Jin-tae is told by his commanding officer that if he can earn the highest award for a South Korean soldier, the Taeguk Cordon of the Order of Military Merit, his brother can be sent home. Jin-tae willingly volunteers for many dangerous missions and is quickly promoted to the rank of Chungsa (Sergeant). His heroic feats during the urban battle of Pyongyang finally result in Jin-tae being nominated for the medal. His combat experiences quickly brutalize him into a cold-blood ruthless killer, which worries his horrified younger brother.
The U.N. coalition is eventually forced to retreat all the way back to Seoul when the Chinese intervene in the war on the North Korean side. Jin-tae gets his medal but Young-shin is captured by a South Korean militia, and the brothers attempt to stop them from executing her for treason when she is accused of having joined a communist party under the Northern occupation. During the struggle, Young-shin is shot dead and the brothers are arrested for trying to rescue her. In the jail, Jin-tae's request to release his brother is refused and the security commander orders the prison to be set on fire when the enemy forces approach. Trying to rescue his brother, Jin-tae loses consciousness and wakes up to believe Jin-seok died in the fire. He brutally murders the surrendering prison commander just before he is captured and restrained by Chinese soldiers.
In truth, however, Jin-seok had been transferred to a military hospital after barely escaping and being saved by a soldier nicknamed Uncle Yang. He learns that his brother has defected to the North Koreans and immediately rejoins the South Korean army to fight at the 38th parallel, but is denied permission to fight. Jin-seok escapes and runs to the North Korean side, surrendering and claiming that he is the brother of Jin-tae, who is now the fanatical leader of an elite North Korean formation known as the "Flag Unit". The North Koreans think Jin-seok is a spy, but as they are about to take him to the command post for interrogation, their position is attacked by American and South Korean forces. After being freed, Jin-seok makes his way through the chaos in search of his brother when the "Flag Unit" arrives to reinforce the North Koreans.
Not recognizing his own brother, the crazed Jin-tae desperately attempts to kill Jin-seok, but is wounded at the last moment. Jin-seok attempts to carry him away but is shot in the leg. Jin-tae then finally is brought back to his senses recognizes his brother, but their reunion is short lived because North Koreans are closing on them. Jin-Tae tells his brother to leave, and Jin-seok initially refuses, but goes after Jin-Tae promises that he will meet him back at home. As the wounded Jin-seok limps away to safety, Jin-tae mans a machine gun and begins firing at North Koreans, covering for his brother before being finally gunned down in a hail of fire.
In 2003, the elderly man stands at the excavation site and it is revealed he is in fact Jin-seok and the remains discovered there belong to Jin-tae. He examines the excavated items, including the long lost silver pen, and begs his brother's skeletal remains to speak to him, quoting his promises as his granddaughter looks on with sympathy. Back in the 1950s, in the aftermath of the Korean War. Jin-seok returns to his mother, sees the shoes his brother finished making, and heads off with Young-shin's younger siblings in a now-peaceful Seoul. He reassures them that he will return to school, thereby fulfilling the promise he made to Jin-tae.

Question: What is the name of Jin-tae Lee's younger brother?
Answer: Jin-seok Lee