Yes you can type out what she calls you, and you can type out the exact MC name there, which I did. However, the game doesn't recognize that you are now having her call you by MC's actual name. It is still treated as just another title by other NPCs.
e.g. I had her calling by my MC name, but during the Lucia pizza delivery BJ scene, Lucia starts using that title rather than your name. She says she heard Lin calling you that, and asks whether you liked it. I was confused at first, because that title and MC name are same in my game, but the game doesn't know that.
As
Ultimate_Mayhem21 mentioned, the game is not able to recognize that the title and MCname are same. This could be fixed by adding an option to have them explicitly start calling you by your actual name.
Ultimately, the issue I have with this is that Lin (and also Android but that is perhaps more understandable) are treated more like not-people than other characters like Nia and Sylvia. This is also obviously reflected by Lin having the Obedience stat, rather than affection or happiness.