WARNING: The following contains spoilers for the Attack on Titan manga by Hajime Isayama, available in English from Kodansha.
As Eren Jaeger fights to change the world in Attack on Titan, he owes a great debt to the man he is named after, Eren Kruger. One of the previous wielders of the Attack Titan, Eren Kruger is single-handedly responsible for, well, the entire series. More so than anyone else, guys named Eren who possess the Attack Titan get stuff done, no matter what it takes. Despite his brief tenure, taking place entirely in flashbacks, Eren Kruger is one of the most important characters in the series.
Eren Kruger is so influential that not only did Grisha Jaeger name his son after him, but Eren also used the name Kruger as an alias when he infiltrated Marley. It's rare that the events of an entire series can be attributed to the legacy of a single man, but Eren Kruger did indeed change the world. Eren Kruger's history, as well as Eren's time posing as "Kruger," speak for themselves when it comes to their impact on Attack on Titan.
Who Is Eren Kruger?
Kruger is an Eldian who was born inside the Liberio Internment Zone. As a child, he watched his father be burned alive by Marleyan soldiers as punishment for being an Eldian Restorationist. Later in life, he managed to join Marley's Public Security Authority with the help of a doctor, who faked Kruger's blood tests to hide that he is an Eldian. Eventually known as The Owl, Eren Kruger led the Eldian Restorationist Movement while continuing his work as a mole in the Marleyan military.
When Grisha Jaeger and his wife, Dina Fritz, are outed as Restorationists by their son, they are sentenced to death by way of being turned into mindless Titans on Paradis Island. After allowing all the captured Restorationists, except for Grisha, to be turned into Titans, Kruger finally takes action and saves Grisha's life. Grisha recognizes Kruger as one of the officers who found him and his sister when they were children and wandered outside of the Internment Zone.
Kruger admits that he saved Grisha because of the hatred he saw in his eyes as a child when the young Grisha first learned that Marleyan soldiers had murdered his sister. Revealing that he is the current Inheritor of the Attack Titan, Kruger decides to pass the Titan on to Grisha so that Grisha may carry out the Eldian Restorationists' mission. Kruger also encourages Grisha to find someone to love inside the Walls so that the broken man will have the will to keep fighting.
When Grisha slaughters the Reiss family and steals the Founding Titan, he starts the chain of events that will ultimately lead to the end of Eldian oppression and the Titans themselves. He was only able to do so because of the Titan powers and knowledge that Kruger passed on to him. If Kruger hadn't saved Grisha's life, the Founding Titan would have remained in the hands of the Reiss family until the inevitable downfall of the Eldian people.
Who Is "Kruger"?
Just like his namesake, Eren Jaeger is willing to do whatever it takes, even turn against his own people, in order to serve the greater good of Eldians as a whole. After receiving memories of the future thanks to the Attack Titan's special ability to transcend time, Eren goes rogue and infiltrates the nation of Marley. Learning of Eren Kruger via his father's memories, Eren Jaeger chooses to further honor the name of the man whose actions allowed Eren to be born in the first place by choosing the alias "Kruger."
Posing as a wounded Marleyan soldier, "Kruger" meets with Zeke Jaeger, his half-brother, to discuss working together. Since Zeke possesses the royal blood that Eren lacks, together they can wield the power of the Founding Titan. Eren's actions in Marley set Attack on Titan's endgame into motion when his attack forces the whole world to unite against Paradis Island, which in turn forces Paradis Island to take immediate action regarding the use of the Founding Titan.
Eren Jaeger's time in Marley is remarkably similar to Eren Kruger's in that they each went undercover while acting on memories received from the future. They each dirtied their own hands in order to carry out their plans, even going as far as to harm their own people. Eren's infiltration of Marley ultimately succeeds in him gaining control of the Founding Titan. His use of the Founder's power, free of the royal bloodline's influence, is exactly what Eren Kruger wanted when he allowed Dina Fritz to die but saved Grisha.