FORTUNE — Even if you use a Galaxy phone, how much do you really know about the company that made it? Can you name Samsung’s chief executive officer? Or, for that matter, any of the conglomerate’s top leaders? Do you have any sense for what it’s like working for Samsung? Do you know how much money it makes or whether it gives any of that money away to charities? Probably not, finds a new survey from Harris Interactive.

The annual Harris Poll Reputation Quotient, published Tuesday, sheds some new light on consumers’ perceptions of smartphone king Samsung Electronics. The Korean company has seen a meteoric rise in smartphone sales and in consumer awareness of its brand. In 2011, respondents didn’t even mention Samsung when asked to name the most “visible” companies. In this most recent survey, Samsung not only made the list, it also topped Apple AAPL in categories like “products providing great value.” But the survey also found that, while Samsung’s reputation has significantly improved, there is a lot consumers don’t know about Samsung — beyond the smartphones, phablets and tablets they are increasingly purchasing and using. And that information gap, despite the company’s recent growth, could turn out to be a problem.

“It’s uncommon, going from completely unmentioned to one of the strongest,” says Robert Fronk, executive vice president at Harris Interactive. “But it’s a tenuous hold. When you are one-dimensional you tend to fall off quickly.”

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Fronk suggests Samsung should work on developing its “softer side” — sharing its corporate and leadership story, not just focusing on products in its outreach to media and consumers. As a Korea-based, global conglomerate, it is at a disadvantage in the U.S., but it can overcome this challenge (just look to Toyota TM and Honda for examples of Asia-based companies that have become beloved brands in North America). And becoming a brand that’s known not just for specific products but for a broader corporate identity takes time.

“Apple built its reputation over time,” says Fronk. “Eventually people made the jump from loving their iPods to loving and respecting Apple.”

Of course, Apple has a network of its own retail stores where customers can interact with Apple employees and get first-person look at the company’s style — down to its detail-oriented approach and minimalistic design. Samsung has opened up a handful of “Galaxy Studios,” where consumers can play around with its devices, though they are ultimately directed to nearby carrier stores to actually make purchases. The company has also made efforts to build its presence in the Silicon Valley, where many members of the tech media reside.

Why should Samsung care about showing more of its “corporate face?” Every company fumbles sometimes (just ask Apple). And when Samsung does, customers who can connect a face to the name may be just a tad more forgiving.

From the survey: