Police said the deceased were Bartlomiej Kuczynski, 45, Kanticha Sukpengpanao, 36, Jasmin Kuczynska, 12 and Natasha Kuczynska, nine.
Post-mortem examinations showed Mr Kuczynski and Ms Sukpengpanao died from stab wounds to the neck.
Norfolk Police has twice referred itself to the police watchdog in connection with the case.
Detectives have said they are not looking for anyone else following the discovery on Friday in Costessey.
Post-mortem tests on the two girls are due to take place on Wednesday.
Earlier on Tuesday, the Independent Office for Police Conduct (IOPC) revealed a man called 999 from inside the property in Allan Bedford Crescent, on the Queen's Hills estate, before the bodies were found and said he was confused and worried about his mental state.
He was advised to seek medical advice and contact the NHS on 111, it is understood.
The initial 999 call was made shortly before 06:00 GMT, but police did not attend the house until about 07:15 when they received a call from a concerned dog walker.
Officers forced their way into the property and discovered four bodies inside.
The IOPC said it would be examining whether the handling of the contact with the caller "was appropriate and in line with force policy, training and procedures".
"We will be making contact with the families of the deceased to explain our role," the IOPC's regional director Charmaine Arbouin said.
Ms Sukpengpanao was visiting the house at the time of the deaths, police said, while Mr Kuczynski lived there with Jasmin and Natasha.
Pupils have been offered support at the two local schools attended by the girls.
Dr Roger Harris, head teacher of Taverham High School, near Norwich, described their pupil Jasmin as a "lovely young lady".
He said: "She was quiet and a little bit cheeky sometimes. But as a parent myself, you'd be very proud to call her your daughter."
Dr Harris said he had asked teachers to think about their seating plans "to be mindful of that one empty seat".
Dr Harris says he wants the school to remember Jasmin but for pupils to also "move forward"
Matthew Cross, head teacher of Queen's Hill Primary in Costessey, which Natasha attended, also paid tribute to her.
"I'll remember Natasha for the way in which she was just so kind and gentle to everybody and I think those values and those qualities just resonated through her," he said.
"She was just one of those pupils you wanted in your class. She was kind, generous and took so much pride in her learning."
Both schools said they had been working with Norfolk County Council's critical incident support team to ensure they had extra provision in place for "pupils and staff at this difficult time."