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.
Vegeta would be a great addition. His rivalry with Goku and his pride as a Saiyan would add an interesting dynamic. He might be initially jealous that Goku is getting to fight and train with the God of Destruction. But then he would also want to prove himself and join in the action. Whis could also be included. His knowledge and calm demeanor could help in situations where the power of Goku and the God of Destruction gets out of hand.
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.
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.
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.
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.
One possible plot could be Goku, in his Saiyan tenacity, challenges the God of Destruction to a friendly spar. The God of Destruction initially scoffs but is soon impressed by Goku's power. As they fight, their powers start to blend, creating new energy forms that threaten to disrupt the balance of their universes. They then have to team up to contain this new energy while also learning from each other's fighting styles.
Another great plot could involve Goku facing off against other Gods of Destruction who don't believe he's worthy of the title. This would lead to epic battles where he has to prove himself not just with his power but also his newfound sense of divine responsibility.