When my daughter was first born her name was “Flicka Leckie” for the first 4 weeks of her life.
At birth, the baby automatically assumes Mum’s surname if the parent’s aren’t married. You have three months in which to register the baby’s name. All the correct papers will be sent to your home within the first couple of weeks of the babies birth, including name registration and any custodial paperwork.
If you’d like more information about preparing for baby to arrive you can click on the link from Skatteverket “For Future Parents”.