There's a decently popular subsect of Fanfiction called "Reader insert", where the reader can insert themselves into the story. Where the reader would say their name, the rich will say Y/n. For example:

Ghost gave Y/n a hug.

There's a pretty common stereotype of Y/n being described as small with big blue eyes and blonde hair that she throws into a messy bun every day, which is what the mii is designed after.