One implication could be a change in Konohamaru's status. He might be seen in a different light by the villagers, having Naruto as his father.
Yes, in some fanfictions, Naruto can be made Konohamaru's father. Fanfiction writers often like to play with relationships and create new family dynamics for the characters.
One implication is a shift in Naruto's character development. He might inherit different traits from Itachi. Also, the relationship between Naruto and Sasuke would be completely redefined.
One implication could be a change in Lucy's status. If ACNOLGIA is her father, she might be seen as more powerful or more dangerous.
It can also impact the relationships in the story. For instance, Hermione's relationship with Harry and Ron might be different. Since Severus has a complex history with Harry, Hermione being Severus' daughter could create some tension or new alliances. Also, it could change how the other characters view Hermione. They might be more cautious or more curious about her due to her newfound relation to Severus.
If Naruto is Kunou's father, it would mean a whole new set of powers for Kunou. Combining Naruto's chakra - based powers with the devil - like abilities in 'Highschool DxD', Kunou could be extremely powerful. For example, she might be able to use Naruto's Rasengan technique along with her own devil powers.
I'm not very familiar with this specific 'Hachishaku' fanfiction. But in general, if Naruto is made the father in a fanfiction, it could bring a whole new dynamic to the story. It might change the relationships of the characters involved and create unique plotlines centered around Naruto's role as a father.
Well, it would completely change the Naruto timeline. Hagoromo was the one who started many of the ninja traditions and powers. If Naruto was his father, it would mean Naruto had a much greater impact on the early days of the ninja world than in the original story. Also, Naruto's values like friendship and never giving up would likely be passed down to Hagoromo in a different way, perhaps influencing how Hagoromo developed the ninja way.
One implication is a change in their power dynamic. If Kurama is a pet, Naruto may seem more in control. Also, it can create more comical situations.
One implication is that Naruto could have access to more powerful jutsu. Since Hashirama was known for his strong Wood - Style jutsu, Naruto might inherit or learn something similar. Another is that he could have a greater influence in the village politics as Hashirama was one of the founders. It could also change the way other characters view Naruto, perhaps with more respect due to his relation to such an important figure.
One implication is enhanced power levels. If Naruto is Hagoromo's reincarnation, he could potentially access even greater chakra reserves and more powerful jutsu. It also means he has a closer connection to the origin of ninjutsu.