One popular trope is the 'unlikely partnership'. The OC might be from a different background than Nami, and at first they clash but then grow to respect and rely on each other. For example, an OC who is a former enemy pirate could end up teaming with Nami to face a common, greater threat in the One Piece world. Another trope is 'romantic tension'. Since it's a fanfiction involving a pairing, there's often a slow - burn romance where the OC and Nami gradually realize their feelings for each other. There can also be the 'fish - out - of - water' trope if the OC is new to Nami's world of piracy and has to learn the ropes, which Nami helps with, leading to their bond strengthening.
A common trope is the 'protector' role. The OC could be very strong and protective of Nami, like when they face dangerous foes. In some fanfictions, the OC uses their unique abilities to keep Nami safe. Also, the 'redemption arc' can be a trope. If the OC has a troubled past, they might find redemption through their relationship with Nami. For instance, an OC who was once a greedy thief might change his ways because of Nami's influence. And the 'shared secret' trope is often used. They might share a secret that only they know, which brings them closer together in the story.