DeSai, 46, was shot dead by police, who said he opened fire on motorists near a shopping center in the affluent West University Place neighborhood on Monday morning.
Authorities have said DeSai was wearing military-style clothing and had Nazi paraphernalia on him at the time of the shooting. They said he was armed with a handgun and that 2,600 rounds of ammunition and a rifle were found in his car. Both firearms had been legally purchased, they said.
Memorial Hermann Hospital said two of the victims were still hospitalized and were in good condition. The hospital said it had released three others. Ben Taub Hospital, where some of the victims had been taken on Monday, could not confirm if any of them were still there.
DeSai, who received his law degree from the University of Tulsa in 1998, had a small law firm that closed about six months ago, according to his former law partner.
Prakash DeSai, the suspect's father, told ABC television's Houston affiliate on Monday that his son had been "upset about his law practice not going well" and money woes.
The Federal Bureau of Investigation has said there was no indication the shooting was linked to a radical group.