I just found the perfect reference!
According to the book titled "They Captured the Moment: Dakotas Photographers 1853-1920", Ole Oyloe was a photographer from 1889-1921 in the town of Brookings.
From 1891-1900, Ole Oyloe was also a photographer in Elkton, which is about 20 miles southeast of Brookings (city). The Elkton studio is the studio he bought from Jarvis in 1891. Elkton is also in Brookings County. So I wonder if some of the photos from this studio may have had the Brookings inscription as well.