Robinhood Markets Inc. named three new directors to its board on Tuesday, as the stock-trading startup laid more of the groundwork for what is expected to be one of the year’s most eagerly awaited initial public offerings.

With its easy-to-use smartphone app and commission-free business model, Robinhood skyrocketed in popularity this year amid market rallies in meme stocks like GameStop Corp. and cryptocurrencies like dogecoin.

Robinhood’s financial performance boomed in the first quarter, with its biggest revenue source more than tripling.

Robinhood has pledged to more than double the number of customer-support agents on staff this year.

Until Tuesday’s appointments, Robinhood’s board looked more like that of a startup than a multibillion-dollar, soon-to-be-public company.

Mr. Rubinstein is on the board at Amazon.com Inc., and Mr. Zoellick is on the board of Twitter Inc. Robinhood’s IPO preparations also involve rolling out a new system that allows users to access new listings, including its own, on terms similar to bigger investors.

Last month, the company debuted that platform when medical-apparel startup Figs Inc. said it would allocate up to 1% of its IPO to individual investors on Robinhood.