When China’s Lenovo Group Ltd. took over fading mobile-phone pioneer Motorola Mobility in October 2014, Chief Executive Yang Yuanqing vowed to restore the brand as a global leader.

Addressing staff at Motorola’s Chicago headquarters after the $2.91 billion deal closed, Mr. Yang told them their talents would propel the combined company to global dominance, recall several people who heard him. Together, he noted, the two companies already constituted the world’s third-biggest smartphone maker by shipments.

Mr. Yang saw the deal as a chance to repeat a success he had a decade before, when Lenovo acquired International Business Machines Corp. ’s money-losing personal-computer division and turned the combined company into the world’s largest PC maker.

Two years after buying Motorola, Lenovo has axed at least 2,000 U.S. jobs. It has fallen to as low as No. 8 globally in the smartphone world, from No. 3. In May, Lenovo reported its first annual loss since 2009, which Mr. Yang blamed partly on restructuring costs after the acquisition of Motorola, with its iconic batwing logo.

“We underestimated the differences of the culture and the business model,” Mr. Yang said in a recent interview.