Is “get + person’s name + ed” a common usage in English to mean “become the person like somebody”?

The example you cited is a pun. It makes sense because 'gore' is a verb meaning to pierce or wound with something pointed (as a horn or knife), as well as a name. In the article, Krugman is comparing Clinton's reputation being 'wounded' by a scandal to a similar situation that happened to Al Gore.

To answer your question, if you're not making a pun, using a name in this context (pronoun + 'ed') would only work if using it would translate into a verb. 'Fukushima-ed' doesn't really make much sense, in my opinion. An example that might work is that if you had a friend named Joey who was well-known for playing pranks, and he played a prank on someone, you might say that person got "Joey'd," meaning that they were pranked by Joey.

Firstly, to answer your question directly: Yes, it is a reasonably common English idiom.

Such words are called eponymous verbs, and are formed by the process of metonymy.

Modern examples include Bobbitted and Tebowed, but there are many other examples using names of real and fictional people alike, such as Bogarted, Borked, Boycotted, Casanova'd, Houdini'd, Heismanned, Lewinsky'd, Pompadour'd, Scrooged, Scully'd - some of which had but passing currency in common usage, and some of which have stayed with us to the point where we don't even realize that "borked" and "boycott" are eponymous any more.

Then there are a few names-via-company-names like Hoovered, Biro'd, etc.

Similarly, there are other words used in an eponymous sense, but only with suffixes like -ize, or as other parts of speech (nouns, adjectives). So we have Gerrymander, Bowdlerize, Spoonerize, Mesmerize, Galvanize, Herculean, Erotic, Chimeric, Atlas, Streisand Effect, Victorian, Chauvinist, Quisling, Faustian, Sisyphean, Quixotic, Diesel...

Somewhat related, though I feel they are using the names in a different sense:

Simon & Garfunkel ("A Simple Desultory Philippic"):

(Or How I Was Robert McNamara'd into Submission)
I been Norman Mailered, Maxwell Taylored.
I been John O'Hara'd, McNamara'd.
I been Rolling Stoned and Beatled till I'm blind.
I been Ayn Randed, nearly branded
Communist, 'cause I'm left-handed.
That's the hand I use, well, never mind!
I been Phil Spectored, resurrected.
I been Lou Adlered, Barry Sadlered.
Well, I paid all the dues I want to pay.
And I learned the truth from Lenny Bruce,
And all my wealth won't buy me health,
So I smoke a pint of tea a day.

...
I been Mick Jaggered, silver daggered.
Andy Warhol, won't you please come home?
I been mothered, fathered, aunt and uncled,
Been Roy Haleyed and Art Garfunkeled.
I just discovered somebody's tapped my phone.

Firstly, to answer your question directly: No*, it is not a common English idiom. This can be better described as "artistic license", where the writer of the headline has taken some liberties (read: bent the rules) with the English language for the purposes of humour.

I wouldn't consider this a particularly clever pun, or a massively useful headline. In fact, I find your pun far better. Not only is the global mindset around Fukushima particularly coherent, i.e it is very well known for one very specific destructive thing, it has a useful similarity to the past tense of a certain expletive.

Also, in English speaking families where people try to avoid swearing around children, people often catch themselves half-way through the word and substitute with similar but benign sounds - e.g. "I went drinking over the weekend, got totally Fuc... uh, Fukushima'd". The hope is that the children won't be taking a new swear word to school with them.

However, one thing I would point out: Using an event like Fukushima in a funny context, metaphorically, would be totally fine. However, if writing a headline about a similar disaster, this kind of title would be considered totally inappropriate - both because the writing style would not be considered fitting to the subject matter, but also because belittling a current event where human lives are on the line would be considered "in bad taste".

(Though, as a caveat: some publications make their money by being in bad taste.)

*Edit: As Dewi Morgan has pointed out that it is a common English idiom, with a litany of examples, I feel I must concede. As they also pointed out, many of these are no longer even thought of as eponymous, as their usefulness as concepts has far outlived the notoriety of the person they are modelled after.

Often, the reason the word emerges is not because something happened to one person that then happened to another; it is more common for the person to make a contribution to society (positive or not) that becomes their major legacy, so that their name is synonymous with the attribute or discovery (their name becomes a metonym). As such, they slowly drift into common usage, rather than being thrust - haphazard - into a headline. So the example in the question, as well as many of the examples given by my fellow answerer, feel like very rough and unnatural uses of the literary technique.

So, in the specific context of the question, I stand by my answer, however wrong it is in general; it is not common to tack "ed" onto the end of someone's name just because something also happened to them - it is more commonly because of something they did.

I am going to say "yes". With a warning.

bork

past tense: borked;

obstruct (someone, especially a candidate for public office) through systematic defamation or vilification. "is fear of borking scaring people from public office?" Origin 1980s: from the name of Robert Bork (1927–2012), an American judge whose nomination to the US Supreme Court (1987) was rejected following unfavorable publicity for his allegedly extreme views.

See the date? 1987. The word came into use right after the issue, Robert Bork's rejection, but fell off as time passed. If I used it now, in a group of thirty somethings, I'd likely get a strange look, as they aren't going to know the reference.

The "person-ed" takes a couple factors in my opinion. A name that actually works (no matter how Sonia Sotomayor's nomination to our supreme court went, I doubt Sotomayored would have been uttered) along with a defining, notable event. Bork's situation made the news in a memorable way.

Other examples may last more or less time, depending on the nature of the back story. Al Gore was known for his failed presidential bid and efforts to save the planet (see any reference to An Inconvenient Truth). Trump is a current event and it remains to be seen how his verb survives.