Congratulations on the new home!
I suppose it depends on how much you like seeing what the other person is up to, or them seeing what you’re up to - not assuming either of you have something to hide but I found it really distracting to have my boyfriend looking over my shoulder all the time so we rearranged our main living area so I have a bookcase wall next to me now
If you are in need of new office furniture I’m a fan of the Ikea Bekant range, they also have dividers you can put along the back of their desks (either half the length or the full length I believe) which might be of interest.
First things first though: you may have to Rock, Paper, Scissors, Lizard, Spock to see who gets to sit nearest the radiator! I always get cold so want to be close to a heat source, if that’s both of you then you’ll either need to develop a rotation system or add another heating source (be that a radiator or something else).
Next: I would experiment to see if you prefer sitting back to back, face to face, or along side one another when working. If you have the space I love corner desks, and they don’t necessarily have to have the corner in the corner of the room either, my boyfriend has his the other way around (corner pointing out into the room, one edge meeting the wall and the other as an “exit”.
I hope you follow up with what you do!