Vegeta could be a great rival. He might see Goku's new position as God of Destruction as another thing Goku has achieved that he hasn't. This could fuel their competitive nature even more.
Obviously, Goku is one of the main characters. He is the center of the story as he takes on the role of a God of Destruction.
Goku becoming a God of Destruction could mean a new look for him. Maybe his Saiyan armor would transform into something more fitting for a god, with a more regal and powerful appearance. His power level would skyrocket, and he could start to have an influence on the balance of the universe. He'd also likely have to deal with other gods, which would lead to some interesting interactions.
Goku does reach a state of immense power in the manga that rivals that of a God of Destruction. However, the specific title and all its implications might not be straightforwardly assigned to him. It's a complex development within the story.
One idea could be Goku struggling to adapt to the role of God of Destruction. He's used to being a protector, so having to destroy planets as part of his new duty would create a great internal conflict.
One interesting 'God of Destruction Goku fanfiction' could be where Goku takes on the role of a God of Destruction in a different universe. He might have to deal with new threats and use his Saiyan powers in unique ways. For example, he could face off against an enemy that can manipulate time and space, and Goku has to find a way to overcome this using his God of Destruction powers.
It could be Zamasu. Since Goku Black was Zamasu in Goku's body in the original story, perhaps a more powerful and enraged Zamasu could be the main antagonist. He might be jealous of the new fused form's power and seek to destroy it.
Another option is Tumblr. There are many Dragon Ball Z fans on Tumblr who create and share fanfiction. You can search for relevant tags such as '#God of Destruction Goku fanfiction' to find posts related to this topic. However, the content on Tumblr can be a bit more scattered compared to dedicated fanfiction sites.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
One interesting concept could be Goku's transformation into a God of Destruction - like form. It might involve new powers and a different way of handling battles.
Loki would also be a difficult adversary. He's very cunning and could use his tricks and illusions to try and outwit Goku. Goku would need to rely on his senses and ki to see through Loki's deceptions.