The boy's name was originally Pham Quang Sang, which means "brilliant" and is common in Vietnam.
But Jolie immediately changed his name to Pax Thien Jolie, a fusion of Latin and Vietnamese meaning "peaceful sky."
The boy takes Jolie's last name, since boyfriend Brad Pitt, the father of her two adopted kids and one biological child, was not listed as a parent on the child's adoption papers.
In Vietnam, couples who are not married are not allowed to adopt, so Jolie made the trip without Pitt.
"I will stay at home to help Pax adjust to his new life," Jolie told the Ho Chi Minh City Law newspaper. "I have four children and caring for them is the most important thing for me at the moment. I'm very proud and happy to be their mother."
Jolie adopted the boy on Thursday, during a ceremony at the Ho Chi Minh City Justice Department, which publishes the newspaper.
Since she arrived in Vietnam on Wednesday night, Jolie has been hounded by a jostling horde of photographers and reporters, who followed her from the orphanage to the Ministry of Justice for Thursday's ceremony.
Jolie said she was sorry that her new son had to be exposed to such a media frenzy and expressed concern about how it would affect him.
"Photographs and press coverage will make him upset," Jolie said in the interview, which was published in Vietnamese. "I'm very worried about that. I would like to say I'm sorry for bringing this into Pax's life."
Jolie's oldest son, 5-year-old Maddox, came with her to Vietnam, where she is expected to stay until next week. Her other children are 2-year-old Zahara, adopted from Ethiopia, and another sister, Shiloh, born to Jolie and her and Pitt in May.
Ever since she was young, Jolie said, she has wanted to adopt children.
"Everyone would agree that children need to have a family," the paper quoted her as saying. "I have the ability to help children fulfill that desire. Why should I say no?"
A nurse at the orphanage where Jolie adopted the boy said staff there didn't realize she and Pitt were superstars when they first visited last year.
"They looked very much like ordinary people," said Bui Thi Bich Tuyen. "We thought that they were just an ordinary couple that wanted to play with the kids and give them presents. They brought lots of toys."
Jolie shared crayons and drew pictures with the kids.
"We could already see that she had a heart for children," said Tuyen, the nurse who had been in charge of raising Pax ever since he was brought to the orphanage as an infant.
The New York Post and the Associated Press contributed to this report.
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