One of his name will be Folke, that I am sure of. Why? Because the King's full name is Carl Gustaf Folke Hubertus. The King's first male grandchild is Prince Nicolas. One of his names is Gustaf. The second one is Prince Oscar. One of his names is Carl. The third one is Prince Alexander. One of his names is Hubertus. So this time it has to be Folke.
Will he be called Folke? I doubt that. If they opt for a name used before in the RF, Wilhelm might be a choice. Prince Wilhelm (1884-1965), Duke of Södermanland, was a younger brother of King Gustaf VI Adolf. Or why not Eugen? Prince Eugen was a younger brother of King Gustaf V. As a runner up we have Bertil, the current King's uncle.
Dukedom? Hard to guess, but I will give it a go anyway. My guess is Duke of Dalarna, since Princess Sofia is from Dalarna.
The King will give us the answers in a couple of days.