• Robinhood's user growth, brand recognition and valuation appear to be stronger than ever despite the GameStop trading chaos.
• The free-trading app gained 3 million users last month alone, according to estimates from JMP Securities and demand for its pre-IPO shares is high.
• "Despite some positive and negative press, everyone in the world knows who Robinhood is. They couldn't have better free advertising," said Rainmaker Securities' Greg Martin.

Robinhood's user growth, brand recognition and valuation appear to be stronger than ever as the online brokerage recovers from the GameStop trading chaos.

Demand for Robinhood shares in private markets is surging as the start-up likely benefited from headlines and mentions by politicians and celebrities. Robinhood added gained 3 million users last month alone, according to estimates from JMP Securities.

"From a brand recognition perspective, who doesn't know who Robinhood is?" said Greg Martin, managing director and co-owner at Rainmaker Securities. "Despite some positive and negative press, everyone in the world knows who Robinhood is. They couldn't have better free advertising."

The company, which pioneered zero-commission trading, is still seen as the main gateway for young investors to access the markets. It is expected to go public later this year amid strong demand for fintech stocks such as Affirm, which had its IPO on Jan 13.

Bids for Robinhood's pre-IPO shares spiked during the GameStop mania last month, according to Rainmaker, which provides financing for shares of private companies. Demand also rose after Robinhood CEO Vlad Tenev testified before Congress last week. It's also the most bid-upon stock Rainmaker sees in the secondary market right now. The demand surge could be seen as a vote of confidence for Tenev as he navigated a public relations disaster.

These bids are not guaranteed, but they tend to be a good proxy for investor interest in companies at a certain price. One of the most recent bids for Robinhood shares came in at $52 per share — up from around $15 per share in September.

Private market valuations are often opaque. They are based on outside investments as a percentage of the company. They can also be hard to calculate without knowledge of a start-up's assets and outstanding shares. But based on that pop in bid prices, one investor told CNBC that Robinhood's valuation could be as high as $40 billion — more than triple its last publicly disclosed number.

"With the amount of capital they now have, I expect the company will be the dominant brokerage going forward, and I think the market will acknowledge that," said Martin, who is also the founder of Liquid Stock. "The valuation could be very large in the very near future which bodes well for an IPO."

Robinhood declined to comment on its IPO timing and valuation.

The Silicon Valley start-up found itself in the middle of a firestorm last month amid the short squeeze in GameStop, which was partially fueled by Reddit-driven retail investors. At the height of GameStop's surge, the millennial-favored brokerage restricted trading of certain securities due to increased capital requirements from clearing houses.

Demand from Silicon Valley

Robinhood's decision to restrict trading was met with outrage from traders online. Still, its private investors flocked to back the company. Some venture capitalists responsible for the $3.4 billion in emergency capital cited the app's ability to add customers amid the trading turmoil.

Three of Robinhood's private investors said there was "strong demand" to get a piece of the company, even as it stared down a public relations and regulatory crisis.

The financing came in the form of convertible debt, sources said. That debt will convert to equity when the brokerage goes public, and those investors will get a 30% discount on the market price. One venture capitalist told CNBC he and fellow investors believed the company would go public soon, and the debt round was a chance to "get in at a discount."

JMP Securities analyst Devin Ryan estimates Robinhood's total accounts are now closer to 23 million, including the 3 million gained in January and 10 million users added in 2020 as investing from home boomed during the pandemic.

Robinhood's Tenev told Congress last week the company had delivered more than $35 billion in realized gains to investors, which implies big growth in customers and customer assets. Its average account size is about $5,000, the company said.

Tenev, who co-founded Robinhood eight years ago, answered questions from members of the House Financial Services Committee for more than five hours last Thursday. The Robinhood chief was tempered in his responses, and calmly explained that the billions in cash injections were needed to prevent a liquidity crisis from happening.

One investor, who asked not to be named because company strategy was private, said Tenev's testimony "went well" despite being "painful to watch at times," due to varying degrees of understanding of Robinhood's business model from those in Washington.

"Robinhood emerged from this — there certainly was a hit on the company but we're fully committed to working through that," the investor said.

Another investor told CNBC that Robinhood backers "are feeling pretty good" about Tenev's performance. After 48 hours of the GameStop saga, he said it was clear the Twitter backlash was "insular" as the company continued to add hundreds of thousands of new accounts that week.

"Growth has been great, despite Robinhood taking the brunt of press and questions from Congress —Vlad's done a great job, and as good as he could have done given the situation," he said. "He was sitting at the nexus of potentially pissing off regulators, customers and competitors."

Some analysts say new regulation could hinder the legal, but controversial, practice of payment for order flow, hurting the IPO's prospects. However, Robinhood investors say its value lies in user engagement, not the revenue model. Investors pointed to its position atop the Apple app store, even as it was restricting customers from trading certain stocks.

"It's the fastest growing consumer app, and has better engagement than social media," another investor told CNBC. "The majority of those new traders won't be trading GameStop."

Robinhood users ... investing in Robinhood?

Some critics, most notably Barstool CEO Dave Portnoy, believe Robinhood's brand — built on democratizing investing — won't survive the GameStop trading halts.

However, many expect retail demand for Robinhood's offering to be strong, given it's the vehicle that lets rookie investors access the stock market with little friction.

Robinhood could hit the public markets by way of a direct listing or through a special purpose acquisition company, people familiar with the private dealings told Bloomberg News. It has also reportedly considered allowing investors on its platform to invest directly in the Robinhood IPO.

Airbnb followed a similar playbook by offering shares to their hosts, and the stock more than doubled in public-market debut because of retail participation. Snowflake was another stock that surged on its first day of trading, which some speculate was due to much higher-than-expected retail demand for the name.

With a public debut in mind, Robinhood is now talking about the future of the investing boom it helped spark. Some analysts have floated the idea of Robinhood launching more banking products, or even mortgages, on the millennial-focused app.

The future may also involve more brokerage firms combining stock trading and social media into their platforms, Tenev told CNBC's Andrew Ross Sorkin at the Dealbook DC Policy conference this week. Brokerage firms SoFi and Public already offer this feature.

As for what happened with GameStop, Tenev called it a "5-sigma" event — meaning it had about a 1 in 3.5 million chance of occurring. Robinhood should have enough capital now to deal with regulatory requirements associated with frenzied trading, he said.

But the GameStop volatility doesn't seem to be going away. Investors poured back into the video game retailer on Wednesday, sending shares up more than 100% at one point.

— with reporting from CNBC's Crystal Mercedes.