According to the New York City Board of Elections, Ms. Trump made the change on Oct. 22, 2018, just ahead of the midterm elections.

“I am a proud Trump Republican,” Ms. Trump said in an interview on Monday, discussing her political evolution and the role her father played in it. “I believe he’s broadened the reach of the Republican Party, which is really important to me.”

That the daughter who has never strayed far from her father’s side would officially register as a Republican might seem obvious. But it was a change from her original West Wing role, when she was viewed by some Democratic elites more as a bridge to moderates because of her more progressive positions on issues like climate change, pay equity and parental leave.

Most Democrats were skeptical of Ms. Trump from the beginning. But the fact that she lobbied her father to keep the United States in the Paris climate accords and helped kill a proposed executive order that would have scrapped Obama-era L.G.B.T. protections in the opening days of the administration gave her a slightly different image than the rest of the Trump family.

Since then, she has become a prominent senior adviser to Mr. Trump, focused on issues related to women in the workplace. But as her father becomes increasingly engaged in his re-election campaign, Ms. Trump has made clear where she stands politically.