“But it quickly took on a different meaning,” Ms. Calvert added. “It became code for ‘mother’ and ‘father.’”

Shortly after Mr. Rotondo filed a charge with the Equal Employment Opportunity Commission, the company granted him the full 16-week leave. By the end of 2017, it changed its policy so that other men could easily claim the full 16 weeks as well. JPMorgan Chase said it hadn’t altered its policy but had merely clarified it.

But Mr. Rotondo’s lawyers kept the case alive in order to reach a settlement that would both provide financial compensation for fathers at the company who would otherwise have taken the longer leave and ensure that the company applied the policy equitably going forward.

“We had input into the training module” the company is adopting for those who administer its parental leave policies, said Galen Sherwin of the A.C.L.U., another one of the Mr. Rotondo’s lawyers. “We wanted to make sure that they’re not sending a message inadvertently that dads are discouraged from taking caregiver leave.”

Reid Broda, the company’s associate general counsel, said in a statement, “We are pleased to have reached an agreement in this matter and look forward to more effectively communicating the policy so that all men and women employees are aware of their benefits.”

Some companies offer long leaves to all new parents — Hewlett Packard Enterprise recently announced that new mothers and fathers would both receive at least six months of paid leave. Others continue to offer substantially longer leaves to primary caregivers.

Since Mr. Rotondo’s case began, JPMorgan Chase has increased the parental leave available to nonprimary caregivers to six weeks. The company allows any new parent to claim either primary or nonprimary leave after signing a notice that includes a date of birth or adoption. Workers can change their status from nonprimary to primary if new circumstances arise.