Given that Sunny Side Up doesn't exist in the ATLA-Universe, it should be cannonical that Zuko looked around the room, saw Iroh drinking tea, and named his Friendfish "Jasmine."
...Why would Sunny Side Up not exist? Eggs exist. Cooking exists. And it's a sun-themed name, clearly superior to whatever the Earth Kingdom and Water Tribes call it. You leave Sunny alone, he doesn't need any hot leaf juice!













