Amazon's private-label push appears to just be taking off, but the internet giant still must prove its brands can hold their own amid a swelling marketplace of goods.

A recent study by L2, a research firm that studies brands' digital performance, has identified more than 40 private brands associated with Amazon. (Some operate under trademarks filed by James F. Struthers, whose name has been affiliated with previous Amazon trademark applications.)

Twenty-nine of those labels are in the apparel space, according to L2. And Cooper Smith, an analyst at L2, has further noticed that Amazon is beginning to call out in search results which brands it owns, labeling items under "Our Brand."

A separate study from retail and brands analytics firm 1010data found that Amazon's private-label products merely accounted for about 2 percent of total units sold on Amazon.com, excluding the retailer's third-party marketplace and subscription services, in the first half of 2017. Amazon didn't immediately respond to CNBC's request for comment on those reports.

All things considered, 2018 is likely to be the time for Amazon to prove the potential of its private-label business.

Many of Amazon's brands have quietly debuted in recent months. The company has been notorious for not promoting an attachment to its brands online — but that could change next year, as the company masters its private-label approach.

"Private label is a big deal for any retailer, [and] if you can execute that's where you can have more control of your margins," Moody's analyst Charlie O'Shea told CNBC. "If you can get a dedicated private-label customer they will keep coming back because that's the only place they can get that brand."

With its razor-thin profits, Amazon could use private labels as a way to finally scale operating margins. Costco's Kirkland Signature, Walmart's Great Value and Target's Cat & Jack are all examples of a similarly successful approach. A private-label line also allows a retailer to learn more about its shopper base — tracking exactly what they want and when.

This past year, Amazon rolled out multiple apparel lines and furniture brands, as it increasingly marketed its grocery labels including Wickedly Prime and Happy Belly, also adding more SKUs — like packaged nuts and spices — to those categories.

In buying Whole Foods, Amazon also acquired the grocer's 365 brand. Even before its purchase by Amazon, Whole Foods had begun to roll out smaller-format stores dedicated to its private label. Analysts and industry consultants are already speculating these locations could become a testing ground for other Amazon-branded merchandise, for example clothing from its newer athletic apparel line Peak Velocity.

"From a digital perspective, Amazon has already increased the shelf space of private-label [products]," L2's Smith told CNBC. "I expect there will be a much larger push next year."

In partnering with department store chain Kohl's to sell the Echo and other tech gadgets, Amazon could further negotiate a deal to use some of the retailer's real estate to sell its own apparel or food brands next year. Amazon also is preparing to launch a fashion service called Prime Wardrobe, which threatens the likes of Stitch Fix and Rent the Runway.

Amid this push, Amazon must be careful not to upset any of its established retail partners as its own products climb up the Amazon.com search ranks, Smith warned.

Amazon has added more established brands such as Nike and Calvin Klein to its website, luring in shoppers who recognize those labels. But while browsing Nike hoodies, shoppers will likely stumble upon Amazon's own.

"Big brands are getting frustrated ... they think [Amazon] is encroaching on their brands," he said.

According to 1010data, one of Amazon's private-label lines, AmazonBasics, delivered more than $200 million in sales during the first half of 2017, making it the company's most successful venture to date. AmazonBasics sells everything from batteries to phone chargers to wash cloths — mainly "everyday essentials" that shoppers are looking to pick up in a pinch.

Amazon Elements, which is known for its baby wipes and vitamin supplements, brought in about $9.5 million in sales, the firm found. Next in line, Amazon's labels including Pinzon for bedding, Happy Belly for snacks and Lark & Ro for women's fashion, each brought in more than $1 million in revenue for the first half of the year, 1010 data reported.

For the time being, many of Amazon's newer private labels are still exclusively sold to Prime members, allowing the company to test what works and what doesn't with a smaller audience.

"My hypothesis is Amazon will find [private-label apparel] difficult until they learn to curate an assortment in a really unique way," Kantar Retail analyst Bryan Gildenberg told CNBC. "I think in a number of categories we will see them learn and get better."

It's no surprise Amazon aspires to grow its own brands. Private-label products have increased sales by 0.7 percent over the past four years, while branded products' sales fell 0.3 percent during the same period, according to Nielsen.

The associated negative stigma and "quality gap" between branded and private-label items is shrinking, according to Nielsen, which found nearly three-fourths of Americans are now saying a store brand can be a "good alternative" to a well-known (typically more expensive) brand.

In monitoring reviews on Amazon's private-label products online, Smith said he hasn't seen too many negative reviews, a sign the quality isn't terribly unsatisfactory. But the lines also haven't reached the point where shoppers are "running home to tell their significant others" about them, he added.

As Amazon looks to grow in grocery, Nielsen has also estimated that nearly 1 in every 5 items sold in U.S. supermarkets in 2016 was from a private-label brand, with store brands accounting for more than $150 billion in retail sales by themselves last year.

A separate report from Cadent Consulting Group is predicting private-label brands could "steal" as much as $64 billion from national names over the next decade, as millennials are becoming more receptive to shopping brandless than baby boomers.

"The way the Amazon model works is a great way to develop a private label," Kantar Retail's Gildenberg added. "I think they'll find success in categories where they can do what they've always done — insert themselves into the value chain and create great economics."