Senator Robert Menendez’s soon-to-be wife dropped a lot of names during a 2019 meeting she held with a lawyer who later paid off the delinquent mortgage on her Englewood Cliffs, N.J., home, saving it from foreclosure.

But Mr. Menendez’s name was not one of them, the lawyer, John Moldovan, testified on Tuesday in the second week of the senator’s federal bribery trial in Manhattan.

Mr. Moldovan said he was later instructed by his boss, Wael Hana, the owner of a New Jersey-based halal meat certification company, to pay $23,568.54 to a lender that held the mortgage on the home owned by Nadine Menendez, who married the senator in 2020.

Mr. Hana never brought up the senator’s name either, Mr. Moldovan testified.

“Never mentioned his name once to me,” Mr. Moldovan said during cross-examination by Mr. Menendez’s lawyer, Avi Weitzman.

Prosecutors, in building a case against Mr. Menendez, have been trying to show that the senator conspired with his wife, Mr. Hana and another New Jersey businessman, Fred Daibes, to take bribes in exchange for political favors. The mortgage payment that saved Ms. Menendez’s home was among the first payoffs, according to the indictment.

Mr. Menendez’s lawyers have offered the jury a far different narrative, accusing his wife of deceiving him about her dire finances and any payoffs she may have solicited from others.