West Yorkshire Police confirmed Logan, three, and Jake, two, died in the fire on Alder Street, Fartown, on Saturday.
A police and fire service investigation is under way but officers said the blaze appeared to be "a tragic accident".
Three fundraising appeals totalling Â£1,500 have been launched to contribute to the funeral and help the family.
They have already raised more than Â£900.
Firefighters were called to the semi-detached house at about 14:00 GMT.
The victims, who are believed to have been in an upstairs bedroom, were later pronounced dead in hospital.
Chris Kirby, of West Yorkshire Fire and Rescue Service, said firefighters were "very upset about the scenes they had witnessed".
Mr Kirby said: "Our thoughts are with the family affected, clearly it's going to be devastating for them [and] the local community.
"There's also an impact on the crews who attended. I was speaking to some of them yesterday, they had tears in their eyes."
The fire is thought to have spread rapidly in the upstairs of the property. It is believed the house had no working smoke alarms.
Neighbour Shaveta Sharma said: "It's been absolutely awful. It's so tragic, an awful experience."
Labour councillor Amanda Pinnock, of Kirklees Council, said: "Because of the area, everybody knows everybody.
"They will be shocked by what has happened."
Two children who died in a Huddersfield house fire have been named as brothers Logan Taylor and Jake Casey.