Jason Hickinbottom, aged 51, has been named as the victim of the blaze in Tipton.
He and his pet dog were both pronounced dead at the scene in Tame Road, while a woman was rescued and taken to hospital.
Mr Hickinbottom's family said in a statement: "There are no words that our family can use to describe the sadness and grief we feel at this time."
Meanwhile a teenager suspected of deliberately starting the blaze has been released on bail. The 18-year-old female suspect is believed to be known to Mr Hickinbottom and the woman he was with.
The blaze tore through the terraced house at around 8.10pm on Tuesday as police and firefighters tried to rescue the occupants.
Two police officers who were passing the house were joined neighbours in trying to help those trapped inside but were forced back by the ferocity of the flames.
The first of six appliances was at the scene in four minutes, where crews were confronted by a “significant” blaze in the first-floor bedroom of the mid-terrace home.
The woman in her 30s was pulled from the blaze by firefighters and taken to hospital suffering from smoke inhalation.
Mr Hickinbottom was the second person to be killed in a house fire in the Black Country in the space of four days, after a woman died at a house in Smethwick on Saturday.
Detective Inspector Adam Jobson, who is leading the investigation for West Midlands Police, said: "This was a traumatic situation for so many people, including neighbours and all emergency services. We're all very grateful for the support and understanding from people in the area.
"Our investigation is ongoing and the priority now is to support the victim's family and establish exactly what happened."
A woman who witnessed what happened after the fire broke out said a neighbour clambered on to the flat roof of a porch and banged on a window to try to alert those inside the property.
The witness, who did not give her name, said: “There was smoke coming from the window and the back.
“Someone climbed on to the (porch) roof and was shouting.
“Then they (paramedics) were trying to help someone at the front and they put a tent up. It was just shocking.”
The cause of the blaze is yet to be confirmed by West Midlands Fire Service.