The two-year-old boy whose sudden death has triggered a murder investigation has been named as Harry House, Dorset Police said.
Emergency services found the seriously ill toddler at an address in Broadmayne, near Dorchester, Dorset, on May 26.
He was taken to Dorset County Hospital, where he was pronounced dead and his death has been treated as suspicious since a post-mortem examination on June 1.
A man and a woman, both aged 21 and from the Dorchester area, are currently assisting police with their inquiries.
They were both known to the child, police said.
Detective Chief Inspector Sarah Derbyshire, of Dorset Police's major crime investigation team, said: "For investigative reasons we are unable to give the results of the post-mortem at this time.
"I would appeal for the family to be given privacy at this extremely difficult time."
An inquest is due to be opened next week.
Extra patrols are being carried out in the area.
Detectives also urged the public to be careful about their social media comments regarding the investigation in light of the arrests.
A spokesman said Dorset Police "would hate for anyone to accidentally impact on the investigation by posting well-intended but inappropriate comments on social media".