This is definitely a lesser-known name for Mary, perhaps because, as you’ve indicated, it’s one that is very specific to Alaska. The title does not refer to an apparition (unlike the well-known titles Our Lady of Lourdes or of Fatima, say), but it does reflect the fact that Mary has been honored in the Aleutian Islands for quite some time.
Though the Catholic presence in the Aleutian Islands is relatively recent (missionaries first came there in the first half of the twentieth century), the Russian Orthodox Church brought Christianity there in the late 1700s. Early Russian monks apparently had a strong devotion to Mary, which was no doubt encouraged by the Catholic missionaries when they arrived. In fact, it’s not clear whether the title Our Lady of Kodiak was first used by the Russian Orthodox community or by the Catholics. St. Mary’s Catholic Church in Kodiak, Alaska has a wooden statue called Our Lady of Kodiak. In this image, she holds both Jesus and a small replica of a Kodiak fishing boat. You can see a picture of this statue here.
Our Lady of Kodiak many not have the drama of an apparition story behind it, but it certainly reflects the universality of Mary. It’s just one more example of the fact that people all around the world honor her, love her, and make her their own.