The man stabbed to death at a flat in Castledawson on Sunday night was Michael McLaughlin, 24, from Hillhead Road, in the town.
The motive for the attack is still under investigation but it is understood that a housewarming party was under way.
It happened at about 2220 BST on the Hillhead Road, just off the main Belfast to Derry road.
A man in his 20s was arrested nearby and is being questioned by police.
Local Sinn Fein councillor Sean McPeake said there should be no place for knife crime in society.
"Thankfully it is not a common offence here within the Magherafelt district but incidents like this are just not on," he added.
SDLP MLA for Mid-Ulster Patsy McGlone visited the scene of the crime on Monday morning.
He said: "This is a quiet, small, rural town and people in Castledawson are extremely shocked that this murder has taken place in their midst.
"Nobody has the right to take life and we certainly do not want this kind of brutal violence in our community."