On the town website, she also invited the public to make comments in the town’s public meeting on Jan 31.

Ms. Herbst, 58, said in a telephone interview that after posting her statement on Jan. 23, she attended the council meeting for the first time dressed as a woman.

“It was phenomenally positive; everyone was supportive,” she said. “We had a fairly packed crowd for a tiny town — there were 15 or 20 people there. I explained to the people who had not just had a chance to see the website, and everybody said, ‘O.K.,' and we went on and had a meeting.”

But as an elected official who was later appointed as mayor, Ms. Herbst said that she was given a “very stern lecture” by the town attorney about laws that govern elections and canvassing, and that she was told not to change her name before the coming election cycle.

Ms. Herbst also said she has received thousands of messages of support, and three negative ones.

Replies to announcements on her Facebook page and the town’s website appear to be supportive, with residents praising her for coming forward in a state where, in most parts, it is legal to discriminate against people on the basis of sexual orientation and gender identity, according to the American Civil Liberties Union.

In January, Lt. Gov. Dan Patrick, one of the most powerful Republican officials in the state, put Texas on the front lines of the nation’s culture wars when he announced the filing of a bill that would require people in government buildings and public schools to use the bathroom that corresponds with their “biological sex.”

Critics said the bill discriminated against transgender people.

Terri Burke, the executive director for the American Civil Liberties Union of Texas, said Mayor Herbst was showing “tremendous courage in discussing her identity with the public.