I feel like I want to place an idea and you will judge it. Just for the funzies. After all, the story is already there, so let's try the plagiarize route. Since most fanfics fall on this. They aren't using "original characters" (I would say they are since those characters are far from what they are meant to be). They also use the same world. I will use the example that I excel at writing romances.
Let's use the Naruto world since it is the topic of the thread. Never written a fanfic, but I feel like they can be either easy or hard to do. Like you said, most of these characters end up being namesakes alone at the end. (If you like a name, just use it instead of using the same characters or butcher of them). For my take in a fanfic, let's pick an MC as the object of the romance since those are easier to tweak, I guess?
Naruto already has high levels of bromance between Sasuke and Naruto. (Don't ask me but I swear those two should have ended together at the end.) It also has romance at weaker levels. Hinata/Sakura simping for the boys. We know that Naruto is "in love" with Sakura for most of the story. (No one can change my mind that his true love is Sasuke.)
I would have that same thing happen, while he slowly falls for the new mc inserted into the story. Have her be someone he visits or a teammate of another team? Something along those lines. Hinata filled that term, but we all know how that romance went. It was basically ignored until the movie when Naruto magically falls in love with her. (Yes, there were a few scenes before that, but I would not count that as falling for her.)
So, we can follow the entire plot to the T, while changing who he loves easily and slowly. Tweaks can be made like making the new MC an extra teammate because of x&y reasons. Heck, have them interact while they are in the town or something like that. Or someone to save like a side mission and that is where they meet. (This one sounds like the best one out of all of them.) Or have her be the temporary teammate over some missions, while they play out the same.
It has to be something that doesn't ruin the main plot or shift it to their view alone too. This is the hard part. Naruto goes to face a baddy, while MC is a spectator because they were injured or something. After all, Naruto is the MC of his story. He is the one who unites and sees everything go through.
I mean the world has to be the same for it to be fanfic, which means the plot has to be almost identical. This way, one doesn't risk changing the personalities of the characters. Sasuke stays the same edgy lord, while instead of focusing so much on the bromance, maybe tone it down a bit and have Naruto look at someone else. While still preserving the desire to save his friend.
Or we could try to write a tragedy by having the new MC fall for Neji. Heheh...
After writing this, I feel like this is stupidly hard to do. So, I will keep to my original takes and worlds. xD