The trouble is getting the world to recognize all that. China wants to upgrade its economy by selling the world higher-value goods such as cars, jetliners, advanced electronics and more. Famous brand names can help open up new markets and convince global customers that Chinese products are as dependable as American, Japanese or South Korean ones.

Huawei (pronounced HWA-way) is already well known at home. The company outsells all others in China, the world’s largest smartphone market. And it is nipping at Apple’s heels to be the No. 2 phone maker worldwide. According to the research firm Canalys, Huawei shipped 39 million phones in the latest quarter; Apple shipped 47 million. But those Huawei devices were mostly low or midrange.

“We see good signs that people have seen the brand change to a large degree,” to one that is “stylish and innovative,” said Glory Cheung, Huawei’s marketing chief for consumer devices. “I think that’s a very good sign for us.”

Still, Ms. Cheung said, Huawei would rather spend on developing smarter features and better technology than on marketing, even as she acknowledged the importance of building an emotional bond with users. The challenge for the company on that last front is significant: Compared with Apple or Samsung, Huawei has much further to go in forging that elusive something that leads someone to commit to a brand.

Even in China, many people still view Huawei devices as good value for the money and not much else.

Li Haoran, a 24-year-old accountant in Beijing, is a longtime Apple user. Would she switch to Huawei?