The Ohio shooter has been identified as Connor Betts, 24, from Bellbrook, Ohio, CBS News said, quoting law enforcement sources.
According to earlier official statements, Betts was killed by police at the scene within a minute after he started killing people with his gun.
According to AP, citing local authorities, Betts wore a bulletproof vest, a mask, hearing protection, and was carrying at least 100 rounds.
The gun massacre in Ohio is the second deadly mass shooting in the United States in less than 24 hours. Over 20 people were killed and 26 more injured after a gunman opened fire in a Walmart in the Cielo Vista Mall in the city of El Paso, Texas, on Saturday evening.
The massacres, now being considered acts of domestic terrorism, occurred just six days after at least 15 people were injured and four people were killed - including two children - during another mass shooting at an annual family festival in the California town of Gilroy.
All three gunmen reportedly used AK-type military assault rifles. Aside from reports of radical manifestos posted online by the shooters, there has been no direct link between the three killers, according to media reports.
US President Donald Trump ordered flags to be lowered to half-staff to acknowledge those killed in the massacres in the states of Texas and Ohio, a statement from the White House said on Sunday. Flags will be also lowered to half-staff at all United States embassies, consular offices, and other facilities abroad, including all military facilities and naval vessels and stations.