Reuben Morris-Laing, 21, was discovered in Robin Hood Street, St Ann's, shortly before 21:30 GMT on Wednesday, and later died in hospital.
A 29-year-old man is being held on suspicion of murder and a woman, 22, is suspected of assisting an offender.
Mr Morris-Laing's family said they have been left "devastated" by his death.
In a statement, they said: "Reuben was a caring, family orientated man who was always in high spirits.
"He was polite and nice to everyone he came into contact with.
"Reuben was also a hardworking role model who had high ambitions. He had chosen his vocation as a carpenter which was influenced by his father.
"We are all devastated by what has happened and life won't be the same without him."
The incident prompted Nottingham City Council's leader to call for tougher penalties for knife crime.
Detectives investigating the murder of a man who was found stabbed outside a shop in Nottingham have made two arrests.