One direction they could explore is she wants to distance herself from her criminal dad and the name "Watson".
If you want to make it extra soap opera-y, maybe they could reveal that The Burglar was known other than MJ's dad Phil Watson! Shades of Spectacular Spider-Man's Black Cat plot but I think the large teen audiences for these movies would lap up the angle of Peter/MJ's star-crossed romance entwined in tragedy and obstacles.