Aaron Doherty, 24, also known as Harry, was assaulted in the Skeoge area of the city on Sunday, July 12.
“We don’t know the long-term, but short-term is he’s no aneurisms,” Aaron’s stepfather Gerry Doherty said.
Police said investigations are ongoing and are appealing for information.
Aaron had been travelling home in a taxi when he saw a gang of about 15 young people throwing “sticks and bottles” at a black dog, his family said.
Mr Doherty said Aaron asked the taxi driver to stop and got out to intervene
Speaking to BBC Radio Foyle, Mr Doherty said that Aaron has been discharged from the Royal Victoria Hospital and is now recovering at home, but has limited recollection of the incident.
Mr Doherty said that Aaron had a number of tests carried out in the hospital following his attack.
He said they have been told by doctors that Aaron has no brain aneurisms but they are unsure if the attack will have any long lasting affects on his brain.“Nobody knows what a brain injury can do to someone down the road,” he added.
Mr Doherty has said to parents in the area to ask their sons whether they know anything about the incident.
He also believes that the young people involved “are not all bad” and that some of them coming forward could prove helpful in bringing Aaron’s attackers to justice.
He appealed for anyone involved, or to those who know what happened, to come forward.
Mr Doherty said the family are meeting police again on Tuesday.
Police said investigations are continuing into the attack.
They have appealed for anyone with information to come forward and contact detectives on the 101 number.