I don't think a PC will ever become emporer. They'd have to pick a canon name for the lore that no one would like.
They sort of did, actually. When the Greybeards name you Dragonborn.
Lingrah krosis saraan Strundu'ul, voth nid balaan klov praan nau. Naal Thu'umu, mu ofan nii nu, Dovahkiin, naal suleyk do Kaan, naal suleyk do Shor, ahrk naal suleyk do Atmorasewuth. Meyz nu Ysmir, Dovahsebrom. Dahmaan daar rok. Long (in) sorrow (has) waited (the) Stormcrown, with no worthy head to rest on.
By our Voice we give it now (to you), Dragonborn, by (the) power of Kyne, by (the) power of Shor, and by (the) power of Atmora-of-old.
(You have) become now Ysmir, Dragon of the North. Remember these words.
or as translated by Arngeir:
Long has the Stormcrown languished, with no worthy brow to sit upon. By our breath we bestow it now to you in the name of Kyne, in the name of Shor, and in the name of Atmora of Old.You are Ysmir now, the Dragon of the North, hearken to it. You are Ysmir now, the Dragon of the North.