What is the name of this AC power outlet?
You have a lamppropp which plugs in to a lamputtag, which I take to mean "lamp plug" for a "lamp outlet."

The link contains pictures of both, including a lamputtag that is a dead ringer for yours.
Now you know what to ask for when you go to the hardware store, or when you shop on line for one.

Those connectors seem to be a specialty of Sweden, designed to make it easier (safer) for a non-electrician to connect a ceiling lamp.



That said, this would probably have been better on the DIY Stackexchange site.