Selecting 'Your place is here' results in the same outcome - Sigurd remains and Eivor becomes the jarl of Ravensthorpe (A Quiet Homecoming).

Do you become Jarl in AC Valhalla?

You are given the decision as to who will become Jarl during a conversation with Vili. Eivor can decide to uplift Vili's confidence by informing him that he should be Jarl, or tell him that Trygve would be the better choice. If you choose to let Trygve live, then you can choose for him to be Jarl.

Does Eivor become assassin?

It's been confirmed that Eivor is canonically female, so we'll be looking at her within this context. Despite her not being an assassin -- as the brotherhood didn't exist at the time -- the term has been used to sum up the qualities of a main hero.