NANCY JOHNSON HORN hadn’t been a parent for long when she started hearing things that made her question the safety of the Johnson & Johnson’s baby products the hospital had sent home with her.

“When my third child was born, I brought my own soap,” said Ms. Horn, a 45-year-old New Yorker who blogs about motherhood and whose youngest is now five. “I wanted to make sure that I had the natural products and brands I could trust with my kids.”

Ms. Horn’s parenting choices reflect a broader trend that’s hurting one of J&J’s few product lines that still carry the company’s trademark name: Johnson’s baby products. Even after addressing public concerns raised by consumer advocates in recent years, J&J hasn’t been able to shake off perceptions.

The latest generation of mothers moved to higher-end organic brands — many of which didn’t exist a decade ago. The result: J&J’s baby care business has lost market shares in the US, and sales slumped 14% in the country last quarter.

“It looks like millennial moms are trying a lot of new organic, natural, and what we’ll refer to as premium-type brands,” Chief Financial Officer Dominic Caruso said on a conference call with reporters last month. “Our team is very much aware of this and has very, very robust plans to relaunch baby (the product line) in the latter part of the year.”

J&J was set to unveil the new branding effort this past Wednesday at an update on its consumer businesses, according to spokesman Ernie Knewitz, who declined to provide more details or to comment on Ms. Horn’s concerns.

Along with other American consumer giants, J&J has been under pressure from consumer advocates who say US efforts to ensure the safety of cosmetics and household cleaners lag behind Europe. The company phased out substances such as formaldehyde, a chemical deemed a “probable human carcinogen” by the US government that used to be included in its baby shampoo. It also pledged to take out parabens, a preservative banned in the European Union, from all of its baby products.

J&J, however, hasn’t been doing what its competitors have — touting their “natural” designation. The largest baby-care product maker in the US has lost market shares for four consecutive years, to 18.4% in 2015, according to Euromonitor International data.

J&J missed an opportunity to modernize the label, said Eleanor Dwyer, research associate at Euromonitor International in Chicago.

“Taking out the scary ingredients is obviously the first step,” Ms. Dwyer said. “The piece that Johnson & Johnson’s really missing is the emphasis on the ingredients that are there.”

For an example of successful branding, Ms. Dwyer pointed to Cetaphil, a skin-care line recommended by dermatologists to adults. When the brand, owned by Swiss consumer giant Nestlé SA, introduced a baby line in December 2014, it went beyond just saying the lotions were paraben-free and emphasized that they contained skin-calming organic calendula extract.

Tom’s of Maine, a unit of Colgate-Palmolive Co. that added a baby care line in March 2015, also illustrates how the category is developing: products that use a limited number of ingredients and transparency about their origins. Tom’s of Maine lists what it calls its “just what is necessary” ingredients and their sources online.

Many of today’s young parents are millennials, but not all. Some, like Ms. Horn, have kids when they are in their late 30s or early 40s. Either way, their choices differ from the generations that have come before them.

“We’re moving quickly to the point where a clean product is the baseline,” said Carl Jorgensen, director of global consumer strategy and wellness for Daymon Worldwide, a consumer-and-retail consulting company in Stamford, Connecticut. Large consumer products makers are “hyper aware” of these new preferences, but changing production and ingredients is a costly, slow process. “As the legacy brands have been losing market share to new upstart brands, they are having to change.”

Actress Jessica Alba’s eco-friendly baby care brand Honest Co. has capitalized on the trend. The mother of two says she co-founded the business out of frustration trying to find good baby products.

The company was valued at $1.7 billion in a funding round last year and is working with banks on a potential initial public offering to monetize its success, according to a person familiar with the matter.

J&J has been working to turn around its broader consumer business — which includes over-the-counter medicines, Band-Aid bandages, Listerine oral care, and Neutrogena hand cream — ever since recalling about 8 million bottles of children’s and infant’s Tylenol in 2009 due to potential contamination of ingredients. Within months, the company’s over-the-counter drug recalls expanded to include Tylenol Arthritis Pain caplets, Rolaids, Motrin, and Benadryl.

The health care giant is also fighting more than 1,000 lawsuits in state and federal courts that accuse J&J of ignoring studies linking talc-based products such as its Shower-to-Shower feminine hygiene product and Johnson’s baby powder to ovarian cancer.

In February, the company lost a $72-million verdict to the family of a woman who died of the disease. J&J has maintained the product is safe.

While the baby care unit’s $2.04 billion in sales last year accounted for only 3% of J&J’s global revenue of $70 billion, the business matters because of its namesake labels — products like Johnson’s baby oil, head-to-toe wash, and baby lotion.

“Clearly, this part of the business is having a tougher time,” BMO Capital Markets analyst Joanne Wuensch said of J&J’s baby care division. “To me, it also seems a little bit lackluster in terms of new products. These are brand names that have been around since we were children.”

Nancy Kelly, a New York City-based, 35-year-old mother of two, epitomizes J&J’s branding challenge. She says she like Ms. Alba’s Honest Co., Burt’s Bees, and the Aveeno naturals brand — which is actually owned by J&J.

Ms. Kelly doesn’t use Johnson’s baby products, however, because she thinks they irritate her kids’ skin. — Bloomberg