I know my message is coming years later, but Lizzie Jacobson/Dahle is my great grandmother. Lizzie and Martin Heieren were the parents of my grandfather, Stanford Heieren. To my knowledge, her name was Lisabet Bertine, Birthday was July 22, 1882. I hope this helps.
I too have interest surrounding the Jacobson/Dahle phenomenon. I looked through US Lutheran church records and found that Lizzie’s parents, Jorgen Jacobson & Betsy Olson signed their name as Jacobson in 1882. Then in 1890 & 1897, they signed as Dahle. I see Peter their son kept the name Jacobson, but all other siblings kept the name Dahle. I don’t know what happened here, but from my perspective it looks like Jorgen changed their last name Jacobson to Dahle. I’m uncertain as my tree doesn’t go back further than Jorgen. Do you know what happened?