I do not want to give it any special name. I just want to post here how I usually prepare my fried rice.
Basically, I heat 1-2 tbsp of oil (depending on the amount of leftover rice; I don't want my fried rice to be swimming in oil), then sautee 1-2 cloves of chopped garlic, then add the rice. No salt added. Sometimes my sons would add soy sauce. (I sometimes use bacon drippings, or even use leftover bacon, usually the fatty parts, instead of the vegetable oil.)
But, in times when I have leftover sauce/gravy from such dishes as beef pares, chicken or pork adobo, Korean short beef ribs, or meatloaf, I save that even if it is just 1/4 cup, because I love using them to flavor fried rice.
Then I also always have in my freezer bags of peas, sometimes I have canned slice mushrooms, which I love adding to the fried rice. I also save some leftover scrambled eggs (even bacon if any) from past day's breakfast, and cut them into strips before adding.
If I have chives or leeks or spring onions, I also sprinkle them on top before serving.
When prepared this way, especially if we add bits of sausage or hotdogs, truly we Filipinos can say, "Kanin pa lang, ulam na!"
My sons already know what to do when we have leftovers which they can imagine to be good with fried rice.