As wiktionary succinctly puts it,
-ski
The suffix “-nik” also having similar use, in English.
My question: would there, by any chance, be any similar term, slang, or add-on used for an American counterpart/ripoff/clone of a Russian thing?
So, like McJob or McMansion, but more specialized?
Shouldn’t the Russianizing suffix be “-sky”? “-ski” is Polish.
Do you really expect Americans to care about that difference, let alone know about it?
Another form of Russianizing is to do Cyrillic substitutions for letters that look vaguely similar. Like COИCOЯDE or BORДT. I doubt this works very well in reverse, though, since they probably don’t think of the Latin alphabet as being particularly exotic.
Over and over, I have been blown away by the wide breadth of knowledge of the members of this board. I would not be at all surprised to find an American who spent a number of years in Russia, who is sufficiently aware of Russian language and culture, that he’d be able to post a reasonable answer to the OP’s question.
But even more than that, I have been impressed by the many posters who post here in perfect idiomatic English, and claim to be non-native speakers. One of them is even more likely to answer the OP.
(And, by the way, there are also a great number of posters here whose native language is English, yet have no physical, legal, or genetic connection to the United States. My time here has done wonder to make me more aware of my own ethnocentricities.)
Yeah, like those weird people from the UK! 
A lot of them speak American real good.
Not what the OP was asking for; but here’s something on a related subject:
Skwerl - It’s a short film about two people having a dialogue in what sounds like American English. Except the words are total gibberish. They just use sounds that are typical of American English to give a sense of what American English sounds like to a non-speaker.
Other somewhat related videos:
British People Do Their Best American Accent
70 People from 70 Countries Imitate Americans
British People Attempting Their Best American Accent
People Around The World Try An American Accent
One would be looking for something peculiarly idiomatic to the culture. Since there isn’t an identifiable idiom of surname construction in British names, and by extension for those in the US that have British heritage it isn’t going to work in the same way. The US has such a wide set of heritages, any sort of defining name construction is impossible. After all, the American inventor of the helicopter was Sikorsky.
But there are other cultural idioms. As an Australian, we have a habit of creating abbreviations for names, usually with the application of only two rules, adding the suffix “o”, or the suffix “ise”, and contracting the rest of the name as needed. So you get Barnsie (Jimmy Barnse), Jacko (Jack), Jimbo (Jim), Bottlo (bottle shop). It was with great joy that we discovered that our illustrious Prime minister (Scott Morrison) could be called Scomo. If you wanted to parody Australian names, this is where to start.
I guess the habit of using gender suffixes, say “o” and “a” in many European languages might provide some inspiration, but it is a bit thin.
But what of the USA specifically? The one that comes to mind is one that always puzzled me as a child, and although largely obsolete, did seem to be peculiar to the US. The suffix “orama”. It seemed to creep into everything for a time. I assume is was derived from “panorama”, and movie culture in general. But then I’m probably just showing my ignorance. Surely there much be other similar more modern ones? Whether they might be recognised in Russian culture is another matter.
We tend to be bilingual over here due to the endless diet of American TV shows.
Dunno Vaughnie - there is a strong strain in the US of German style surnames paired with slightly obscure first names and a middle initial, going several generations - in the form Lonny J. Frankenburger III, which you’d never mistake as someone from actual Germany.
No definitive answer, but it wouldn’t surprise me if “Yankee” or “capitalist pig-dog” weren’t in there somewhere.
Oh yes! Very good.
Even more so, J. Lonny Frankenburger III. That habit of using the middle name prefixed by the initial of the first name. Or using Jnr on the name.
There’s even a TV Tropes page:
I’d say the best way to make words stereotypically American is to add “American”, “Ameri-” or “Freedom” to it.
“We don’t eat goulash, we eat American goulash! You can tell the difference by the Velveeta!”
“Freedom Fries! They’re like French fires with less surrender!”
“Ameri-do Karate is the best karate!”
pumpkin spice borscht
My profound insight has been reduced to repeating a trope!
I remember the band “Icehouse”, apparently possessing a similar sound to Ultravox, being dubbed “Ultrabruce”.
Hence referring to an ambulance paramedic as an 'ambo", or a garbage collectors as a “garbo” (particularly cute, as one can well imagine the job might make them “want to be alone”).