He was Kenneth Barnard, aged 67.
The blaze ripped through the building in the suburb of Newtown early on Tuesday morning last week.
Police have now removed five bodies from the site but are yet to confirm a final death toll.
Kenneth Barnard's family released a statement through police: "Kenneth was our brother, he was a funny little kid, a kindly boy who became a kindly man as he grew up.
"His nephews and nieces adored him. His phone calls were always caring, and he was very patient when teased, which some of us did every time the opportunity presented itself.
"Rest in peace dear brother, we will really miss you."
Police extended their condolences to his whānau and friends and said the investigation into the fire was continuing.
Police have released the names of three other men who died in the fire: Michael Wahrlich (67), of Wellington who was known to many Wellingtonians as 'Mike the Juggler', Melvin Joseph Parun (68) and Peter Glenn O'Sullivan, aged 64.
A man appeared at the Wellington District Court on Friday last week charged with two counts of arson - one in relation to a couch fire on the third floor of the hostel on the Monday night before the major fire and the second in relation to the blaze set on the building itself.
