A nanny’s immigration or income status can also be a deterrent. In the last nine years, Oliver Quillia, a producer and father of two in the Bronx, has posted exactly one photo on Instagram of his beloved nanny, Lynn, whose last name he withheld for similar reasons. “If it weren’t for the ‘under the table’ pay we give her, I would probably post way more photos of her,” Mr. Quillia, 47, said.

But when oversharing parents omit nannies on Instagram or Facebook, it can indeed be intended to shape perception of their own characters. “I think many of us on social media, probably subconsciously, want to perpetuate this idea that we’re doing it all on our own,” said Natalia Mehlman Petrzela, an associate professor of history at the New School and a mother of two.

Ms. Petrzela is a self-described “exhibitionist” on Facebook, but it wasn’t until five years after she and her husband hired their nanny, Nancy Peter, that she realized she’d never posted a photo of the woman they consider a “third parent.” (Ms. Petrzela’s husband hadn’t, either, but he’s not active on social media).

“My children respect and love her so much, and I do too,” Ms. Petrzela, 39, recalled thinking. “Why am I making that invisible?”

Ms. Petrzela, who is white, had also considered the racial context between her and Ms. Peter, who is Afro-Caribbean. Though Ms. Petrzela is confident their relationship is respectful, “the history of white families being ministered to by women of color is not a really beautiful history,” Ms. Petrzela said. “Part of me felt hyper-aware about even the impression that any of those dynamics are repeating themselves in our home.”

While Ms. Peter is not on Facebook, she said she appreciates being included. “It makes me feel part of the family,” she said. “I did not give birth to the kids, but I love them very much.” Of other parents who don’t want pictures with their nannies, she said, “It’s not fair. I’m going to tell you the truth: most parents feel that if the children are too close to the nanny, that they’re losing something.”