It says in the Mishnah (Sanhedrin Daf 21b):
וכותב לו ס"ת לשמו
— that a Sefer Torah should be written for the King "l'shmo". What does l'shmo in this case mean: for the "sake of the King"? However, what does this mean exactly and why is this done? Why must the King have the Sefer Torah written for "him".
(In the original question I wrote that perhaps there is an intention here that it should be written "l'shmah" like any Sefer Torah (for the purpose of writing a Sefer Torah)? However if this is the explanation that we write a Sefer Torah for the King and it's done "l'shmah" (for the sake of the mitzvah of writing a Sefer Torah), then why does the Mishnah have to point that out? Seemingly this is not the explanation of the words of the Mishnah. Especially since it says "l'shmo" with a vav.)