Þórarinn B. Þorláksson (1867-1924) I know that Þórarinn was the artist because it says so on a plaque right next to the painting. The plaque also says that the portrait was a gift from the University of Iceland (to the National Library?) in 1994.
Source: I (Haukur) took a photograph of this portrait today (May 16, 2008) at the Icelandic National Library. It's currently downstairs by the clothes' hangar near the manuscript department. License: Author died more than 70 years ago public domain images CC-PD-Mark