I think I know what you mean...but can't be sure.
You want to write an FF where the reader is in the story of the movie of show you write about. Am I right? like an OC character, there is the reader. Get what I mean?
Most people then do this.
FFC (fanfiction Character Name)
Y/N) Your name
FFC comes into to the room and smirked, "hi Y/N, you look lovely."
FC is where you out the character of the movie/tv show, like Sam or Dean from Supernatural.
Y/N is the reader's name and you don't change that.
So let me try again:
Dean walked into the room and smirked, "hi Y/N, you look lovely."
That is how most FFs writers write. They don't mention the readers name since they don't know it. So they use Y/N, instead.
You can read many of this fanfiction on http://archiveofourown.org Just search the FF character's name and then the reader.
Dean Winchester/reader...in the search bar and many FFs will come up, believe me.
Fanfiction.net is also a good site to read FFs.
About reader's appearance, don't mention that. Not hair or eye color, since you don't know it. You can mention that the reader push her hair back over her shoulder.
Y/N pushed her hair over her shoulder with a playful grin.
Get what I mean? don't mention all this "Y/N eye color there" that would be too strange and weird to read. Just stick to not mention any color of the eyes or hair.
I hope you understand what I mean. Just stick to Y/N as the readers name, that is how most if not all FF writers do.
UPDATE: Also when I think about it, you can take the gender you choose for your FF. If it's a girl, then do like this.
Dean walked in and saw her sitting on the couch, he smirked, "hello Y/N."
Get what I mean? :-)
Good luck and writing.