It’s been more than a month since Dunkin’ Donuts was rechristened Dunkin’, but a Broad Street store two blocks from our office apparently didn’t get the memo. The sign in front still reads Dunkin’ Donuts.

Presumably, someone will get around to updating the sign in due course; meanwhile, they have a high-traffic eatery to run and that takes priority. But could leaving the wording unchanged be read as a deliberate act of resistance and rebellion?

The fact is, no matter how strategically on target, corporate rebrands almost always raise hackles. Franchisees push back against perceived home office hegemony. Business writers wax snarky. And the tweetosphere lights up with angry comments from customers nostalgic for the past and pained by the loss of a familiar and cherished name. Boston Magazine labeled “Dunkin’” “an unfinished thought,” and a “disyllabic horror.” And Inc. weighed in with disdain for WW, Weight Watchers’ recently slimmed-down moniker, calling it “hard to tag, hard to remember, hard to pronounce.”

But, really, are names worth getting exercised about? Isn’t it the product that matters? When New York news junkies vented their ire about Time-Warner Cable’s plan to rebrand NY1, its all-news channel, a few years ago, a company executive attempted to calm the waters by explaining that “this is a brand-name decision and not a change in content.”

But anyone in the business of helping companies build and strengthen their brands knows that you can’t alter a product’s name—and thus its brand—without affecting the product itself. Rebranding a product impacts the way consumers experience it as well as the way the sales force interacts with their customers.

Of course, that can be a good thing. (This is probably a good place to point out that the Dunkin’ Donuts name replaced “Open Kettle” back in 1950—and that the open kettle canning process is now universally regarded as dangerously unsanitary.) Rebranding that reflects changes in a company’s market, strategic direction or product platform can pay off in heightened relevance and visibility, not to mention increased profitability and ROI. Think Google (which came into the world as BackRub) or Pepsi (originally “Brad’s Drink”).

The point is that a brand isn’t simply an embellishment, like a pocket square or a sprig of parsley, nor can it be neatly cordoned off from the underlying product. Fiddle unnecessarily with a strong brand and you risk squandering equity that’s been built up over years. Just ask Netflix, which lost nearly a million subscribers in 2011 when it split off its streaming service and rebranded it as Qwikster. Or Britain’s post office, which canceled “the Royal Mail”—a name that had served the country well since 1635—and replaced it with “Consignia.” Outrage was so widespread that “Royal Mail” was restored a year later.

Over a half-century ago, Marshall McLuhan said that the medium is the message. In today’s hypercompetitive marketplace, the brand is the product, and when you tamper with one, you tamper with both. Over time, a name change can—and often does—turn out well, with lasting benefits for customers, franchisees and shareholders. But in the beginning, as the company formerly known as Dunkin’ Donuts will tell you, don’t be surprised if it also leaves a bad taste.