Jamie Nicholson, of no fixed abode, is accused of murdering Belinda Dalby.
Nicholson, 30, spoke only to confirm his name at the four-minute court hearing.
His Honour Judge Guy Boney adjourned the case for a plea and case management hearing on August 28 at the same court.
Nicholson was remanded in custody.
The body of Miss Dalby, 26, was discovered in Jordan House, Millbrook Road East on Friday, June 13.
The former Alderman Quilley grew up in the Eastleigh area and been staying at Jordan House for a couple of months, having moved around a number of times in recent years.
Miss Dalby's family paid tribute to her, describing her as a "bubbly" and "popular" person.
Her sister Shannon, 20, said she was "really outgoing and was the life and soul".
She leaves behind four siblings - Shannon, Christopher, Madeleine and Marc, dad and step-mum Grant and Theresa Barrass, and grandmother Ruth Murry, who all still live in the Eastleigh area, as well as mum Sandy Ablewhite, who lives in Brighton.
Her father Darren Hallett, who lives in Lowestoft, Suffolk, and only met her when she was 18, said she was a "very loving person.