Iran Press/ Iran News: James Cho died alongside his parents Cho Kyu Song, 37, and Kang Shin Young, 35, according to reports. His six-year-old brother was injured but survived.
The identifications come as officials probe whether the killer had links to any far-right organizations or beliefs, BBC reported.
Eight were killed in the shooting.
Several victims remain in the hospital.
A verified GoFundMe page says that the Cho family were at the Allen Premium Outlets mall on Saturday to exchange clothing their six-year-old son had received as a birthday gift a few days before.
"An afternoon that should have been filled with light, love and celebration unfortunately was cut short by another mass shooting massacre," friends of the family wrote on the page.
Korean consulate officials in Texas told the Dallas Morning News newspaper that the Cho family were American citizens of Korean descent and that diplomats are in contact with their family members.
Primary school pupils Daniela and Sofia Mendoza, who were sisters, were also killed. Their mother, Ida, remains in hospital in critical condition, according to CBS News, the BBC's US partner.
Aishwarya Thatikonda, a 27-year-old engineer from India, was also killed during a visit to the mall with a friend, as well as security guard Christian LaCour, 20.
On Monday evening, Texas authorities identified the final victim, a 32-year-old male named Elio Cumana-Rivas.
He was from Dallas, Texas.
Six people were pronounced dead at the scene in the north Dallas suburbs, while two died later in hospital.
The 33-year-old suspect, Mauricio Garcia, was shot dead by a police officer who was responding to an unrelated call, ending the attack.
Investigators are now reviewing social media to look into the killer's beliefs, reports CBS.
During the attack, the rifle-wielding attacker wore an insignia which has been associated with hate groups, as well as combat tactical gear.
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