Megan Betts, 22, was confirmed as being among the dead at a news conference at which the victims were named.
At least 27 people were injured in the shooting, the second in the US within 24 hours. At least 20 others were killed in El Paso, Texas, hours before.
Police shot dead the Dayton gunman at the scene within a minute of him opening fire.
Officials said they were still investigating possible motives.
Connor Betts opened fire at 01:07 local time (05:07 GMT) in the Oregon district of the city centre. He wore body armour and came carrying extra ammunition for his .223-calibre assault rifle with high-capacity magazines, police said.
“It’s hard to imagine that there was much discrimination in the shooting… it happened in a very short period of time,” Assistant Police Chief Matt Carper said.
Nearby hospitals had received 27 people and discharged 15 by 10:00 local time.
The Gun Violence Archive, which categorises mass shootings as four or more people shot or killed, says there have been 251 so far this year.
Who was the attacker?
Hours after he had been named by the media, police officials confirmed the shooter’s identity as 24-year-old Connor Betts from Bellbrook, Ohio.
Police searched his house on Sunday.
Officials also listed the victims at a news conference, confirming to a reporter that 22-year-old Megan Betts was the gunman’s sister.
US media reported that she was found dead in a car with her boyfriend.
“We don’t know the thoughts of the shooter,” Mayor Whaley said.
FBI agents are also assisting police with the investigation.
What’s been the reaction?
At a series of news conferences, Mayor Whaley asked people to think of those people “who went downtown on a Saturday night and thought they’d be safe”.
She said that the Oregon district was “one of the safest places in the whole region”.
“Frankly, we’re at a situation now in our country that these are so random,” she said.
She also said the city had gone through a “really tough year”, drawing a comparison to a series of 14 tornadoes that hit Dayton in March.
“What really goes through my mind is one seems completely preventable,” she said. “I just question when is enough, enough.”
She earlier tweeted that she was “heartbroken” after the shooting, and thanked first responders.