It could be an original character created specifically for the fanfic. Maybe a powerful female entity from a long - forgotten clan with a deep connection to war.
In the 'naruto trained by goddess of war fanfic', Naruto could be exposed to a whole new level of power. The Goddess of War might introduce him to some ancient and powerful jutsu. Also, his mindset towards fighting could change under her training, becoming more strategic and less impulsive.
Kosuke might be a character created specifically for this fanfic. He could be someone with a unique background, like perhaps he was once a disciple of a great ninja but then went on his own path. And now he sees potential in Naruto and decides to train him. He could have abilities that are different from the main characters in the original Naruto series, which is why he has something new to offer to Naruto in terms of training.
In this fanfic, Lilith could be an original character created by the author. She might be a powerful and mysterious figure with special abilities that make her suitable to train Naruto.
She could be someone with a special bloodline or ability. Maybe she has a unique form of chakra that gives her certain powers. In the context of training Naruto, her skills and knowledge are what make her important. She could be a mysterious figure who has been observing Naruto for a while and decides to take him under her wing to help him reach his full potential. For instance, she might have the ability to see the latent potential in others and wants to shape Naruto into a great ninja not just for his own sake, but also for the greater good of the ninja world.
It could lead to Naruto becoming even stronger and more skilled than in the original story. Jiraiya's training methods might unlock new powers for him.
She could be an ancient Celtic goddess, like Brigid. Brigid is associated with magic, healing, and smithcraft in Celtic mythology. In the fanfiction, she might see Harry's potential and decide to train him in her unique magical arts.
It could be really exciting. Guts' brutal and unyielding training methods might make Naruto even stronger. Naruto could learn to face his enemies with more tenacity from Guts. For example, Guts' way of fighting in close combat could be incorporated into Naruto's combat style, adding a new dimension to his abilities.
Well, Naruto might become extremely powerful in terms of his mental manipulation skills. Aizen is known for his cunning and ability to deceive. Naruto could learn new ways to outwit his opponents. He might also gain some unique combat techniques that are more psychological in nature, rather than just relying on his physical strength and ninjutsu.