BEIJING—One of Ivanka Trump’s companies applied for a wide range of new trademarks in China in March, a day before she was named a White House adviser, according to previously unreported Chinese filings.

The 14 trademark applications cover sectors ranging from construction to legal services to alcoholic beverages except beer. If approved, they would allow Ms. Trump to widely expand her business in the world’s second-largest economy—or guard against opportunistic local companies seeking to use her name.

Ms....