Ms. Stewart-Cousins also does not often bring up the story about her ubiquitous colorful scarf, which she started wearing so that people would be able to tell her apart from the other black female elected official in Yonkers.

In an interview, she said she had not built her political career around her identity as an African-American woman, in part, because it would have been a mismatch for her district.

As she did with Mr. Cuomo last year, she more often emphasizes her geographic roots rather than her race or gender. (Dani Lever, a spokeswoman for Mr. Cuomo, said that no one was offended at the meeting.)

If Ms. Stewart-Cousins wanted to seize on identity politics, an opportune time arose last year, when Daniel S. Loeb, a billionaire political donor, likened Ms. Stewart-Cousins’s opposition to increased charter school funding as doing as much harm to black people as the Ku Klux Klan.

While some, including Mayor Bill de Blasio, said Mr. Loeb should resign from the board of a charter school group, Ms. Stewart-Cousins stopped short of echoing that call.

Yet at certain moments, in front of certain audiences — a women’s business group, a Black Westchester Magazine radio show — she acknowledges her own story. And it becomes clear that it is never far from her mind.

“People assume that we’ve had a certain consciousness for a very, very long time, and the reality is that we have not,” she said of the recent importance of diversity in public life. “We have constantly had to assert our version of the dream for ourselves.”