I do not know any numbers, but there are definitely native Alaskans with Russian surnames. The ones I met belong to the Russian Orthodox Church near Eagle River Alaska. Perhaps they (their ancestors) were given Russian names upon converting, or perhaps they intermarried Russians. I don’t know.
Just a footnote, really, but anyone interested in the Russian history in North America who can’t make it up to Alaska can visit Fort Ross, on the Northern California coast. (On the ahem Russian River, in fact.)
It was founded by Russian seal and otter hunters and was a thriving outpost of Mother Russia until the hunting was pretty much depleted, at which point the installation was sold to John Sutter.
Many of the Russian army uniforms that came with the deal ended up on Sutter’s private army of (mostly) Native Americans, who were commanded by a Prussian.
Most people are as surprised to learn the Russians had a well-established colony in the mainland US as they are to learn the US invaded Russia in the 1920s. 
I know this is completely a nitpick, but indigenous Alaskans refer to themselves as Alaska Natives, not Native Alaskans. A native Alaskan is just somebody who is born there.
I’d also question your earlier comment about the Native population crossing the Bering Strait as recently as the 1940s. Can you provide a cite of some sort for that? That’s one rough patch of water and ice, and I’ve never heard that claim before. While there may have been people traveling between Little Diomede Island and Big Diomede Island, I don’t see it happening between the mainlands with any frequency after the land bridge was submerged.
Not only are there descendants of Russian colonists in Alaska, but they go down as far as Southern Oregon and Northern California, hence towns like Sebastopol among the Spanish names in the Russian River Valley. The valley itself (named after the river originally called Slavyanka by the explorers from the Russian American Company led by Ivan Aleksandrovich Kuskov) was thoroughly explored and several emplacements established including what would become known as Fort Ross.
As for Sarah Palin, she wouldn’t know a pierogi from ravioli and would probably start an i ternational incident by confusing the Pope with Putin. That a comedic impression cannot be sufficiently exaggerated to distinguish from the perception of what Palin might have said is itself evidence of her ineptitude.
Stranger
Which is, in fact, actually true.
I caught that. Nicely put.
When most people think of Alaska, they think of the Eskimo people, but in fact, as you have obliquely pointed out, the intermingling of Russians with indigenous people was most likely with Aleut, Tlinget, Tshimshian, and other Indian tribes of Southeast Alaska and the western states. That doesn’t mean there was zero interaction with the Eskimos by Russians, as whalers and sealers routinely went to the more northern parts of the territory.
On an anecdotal level, my father, who was a bartender in Juneau in the 40s (and possibly earlier), related stories to me of Russians that he dealt with. I have no idea if they were more recent arrivals or not.
Did all the citizens of Alaska become US citizens when it was purchased? There may have been US citizens there at the time, but the majority of people whatever their background weren’t US citizens initially. Were the Alaskan natives all Russian citizens?
As a US Territory, it’s logical that they would all have become instant US citizens. Prior to the sale, I would suspect that Russia considered them all to be subjects of Tsar Alexander. Not that the Natives cared one way or the other what the white man called them.
Not necessarily, because Native peoples in the continental U.S. were explicitly excluded from citizenship by the 14th amendment (passed in 1968). They wouldn’t get it until the Indian Citizenship Act of 1924.
I’m sure you meant 1868, not 1968. 
I’m guessing that in the latter times, travel across the strait was by aircraft, or at least that’s what I’m gathering from the rest of the article. That’s probably in the top three of the harshest 82 miles on the planet, and I seriously doubt that kayaks and umiaks would be up to the task. In the winter, the pressure ice would prevent any meaningful surface travel. Interesting article, though.
It’s hilarious, I was going to post about my old boss who was a Russian from Alaska. His last name is Kvasnikoff!
He also had a great deal of Native Alaskan blood in his ancestry as well. This jives with what others have said in this thread.