Argthtjtr

Example: A character owns a pair of Sophia Loren sunglasses. Before going out for the afternoon, "She drew on her Sophia Loren’s, flipped her long mane back, and tossed him a cheeky grin."

If I'm not mistaken, this is an example of a "proprietary eponym". Is the apostrophe correct here, or should it be "Sophia Lorens"—i.e. since the thing referred to is a plurale tantum, should the proprietary eponym also take the form of a plurale tantum?

What if it were a Sophia Loren hat? I doubt that anybody would be inclined to say, "She put on her Sophia Loren's," or "She put on her Sophia Lorens." Despite the question of punctuation, it's likely they would say "She put on her Sophia Loren"—or, perhaps less awkwardly, "She put on her Sophia Loren hat." And, in response to "Hey what kind of hat is that?" it would likely be more common to hear, "Why, it's a Sophia Loren!"

So, I don't think that if the singular form is punctuated without an apostrophe, that the plural form would be.

Still, syntactically, it's a pair of sunglasses, and whether it's a single object that's being referred to or not, I think that rules of pluralization apply.

Normally, this would be a matter of style, and it would follow the rules of whatever style guide you use.

If using Sophia Loren as a noun, The Chicago Manual of Style would say that the plural should be Sophia Lorens.

However, in this case, there may be something else that determines how it should be handled.

From Mignon Fogarty's article "How to Make Product Names Plural":

Product names are usually trademarked, and companies don’t like you to use trademarked words generically. Making names plural counts as using them generically. . . . In other words, Apple has always said it wants you to say things like “I have two iPad Pro devices.”

Also per that article, however, "we all know that’s not realistic in casual writing and speech."

But if you don't have a style guide that you follow, and there is no guidance on the trademark of the item name—or even of the use of the company name in general—it's really up to you how you choose to pluralize it. Of if you simply rephrase the sentence to avoid pluralization altogether.

Just want to make a point. You said that this was a case of a "proprietary eponym". I haven't heard of this term but the definition I found shows that it's another term for "genericised trademark".

proprietary eponym
A successful brand name or trademark that has
come into general use to refer to the generic class of objects rather
than the specific brand type... For example, kleenex is used to
describe many types of facial tissue.
Wiktionary
definition

You'll find the same thing here:
Generic trademark

I would say to call your glasses Sophia Lorens might be a case of metonymy, ie., naming the glasses after something related to the glasses.

Jason Bassford is right about the use of the singular and plural with his hat example. Also, following Hot Licks' example you can see the pattern that your glasses/spectacles, and Nikes/shoes, are plural, they are a pair of glasses (strangely), and pair of shoes; that's why you'd call them your Sophia Lorens, not your Sophia Loren.

On the topic of apostrophes, the general rule is to not use an apostrophe to indicate plural. So if you have a Sophia Loren handbag and then buy another, you'd say "check out my Sophia Lorens." Maybe a bad example, but you get the point.

The rule of not using an apostrophe to make plural is broken often enough, including by me, if I find the strict rule is more of a hindrance than a benefit. I believe "two SOS's" is easier to read and understand than "two SOSs". Also, take for example the expression "Mind your Ps and Qs." It may look better as "Mind your P's and Q's."