NEW YORK – Joann Prinzivalli has gone through a lot to be a woman, and she wants her birth certificate to show it.

Born Paul Prinzivalli Jr., she says she knew her true identity was female by the time she was 4 and broached the subject with a mental-health adviser as a teenager. But it was decades before she bucked family expectations and social pressures, changed her name and underwent electrolysis and hormone treatment to make a change that cost Prinzivalli her spouse, family, home and job.

About 10 years later, she’s still a man in one important context: on her birth certificate. She’s been unable to change the gender listed on the document because of city rules that she and some other transgender people call discriminatory, intrusive and out of step with recent moves by the federal government and some states to make it easier for transgender people to change ID documents.

“Knowing that it was a mistake in the first place, and having that fixed, is pretty important to me,” the 57-year-old title insurance lawyer said Monday as she sued the city. Two other transgender people have filed similar suits in recent days, and a third plans to do so.

They are contesting a city Health Department practice of requiring people to undergo genital surgery and a post-surgery psychiatric evaluation before changing the gender on their birth certificates, according to the lawsuits. Many transgender people can’t have that surgery for medical or financial reasons, and having hormone or other treatment to change gender should be enough, the plaintiffs say.

City lawyers say officials are trying to make sure there are checks on changing an important identity document used for citizenship, Social Security and passport purposes.

“Although we understand the concerns … the Board of Health should not change its requirements without assurance that the amended certificate cannot be misused,” said Gabriel Taussig, a city lawyer. He was responding to a lawsuit filed Monday by Louis Birney, a 70-year-old transgender man. Birney had genital surgery but objects to the requirements for detailed documentation and a psychiatric report, calling them violations of medical privacy.

Updating ID documents has long been an issue for transgender people. Varying local, state and federal rules sometimes mean a person’s sex changes from birth certificate to driver’s license to passport. The patchwork result can cause a host of problems in a security-conscious time when IDs are increasingly demanded and scrutinized, whether for boarding a plane or getting a job.

Transgender-rights advocates and others, including the National Association of Social Workers, have encouraged agencies to abandon surgical requirements.