Then they started investigating "Anders Behring Breivik".
Simple police work.
Video captured him leaving the car (bomb) while wearing police uniform. He even had fake police ID with name Anders, ID he used when asked for ID 2 hours later, before going onto the boat to Utøya.
When it was reported that a man dressed in police uniform was killing kids on Utøya 2 hours later, police suspected it could be the same person. After he was arrested, there was no doubt who he was. He never tried to hide his identity, he wanted his name known.
The whole bomb + massacre was just a PR to make sure his Manifesto gets published around the globe.