Reno Deputy Police Chief Tom Robinson has said the gunman didn't appear to be targeting people. But because the shooter didn't open fire until he reached the exam room area on the third floor of Urology Nevada, police said the incident didn't appear to be completely random.
Gholdoian was a 46-year-old urologist. Authorities previously had reported a doctor being wounded in the attack.
Spears was a 20-year-old relative of a patient.
"Urology Nevada is shocked and saddened by the events that occurred," the center's statement said. "At this time we have no information as to why these terrible events occurred, and we are cooperating with the authorities in every way possible to learn more."
Robinson has said there were about 100 people in the facility when the shooting happened.
Investigators have said they were confident no one else was involved. The shooter used a 12-gauge shotgun in the spree and fired five rounds, including the one that killed him, police said.
The shooting comes nearly two months after a 12-year-old boy opened fire at an area middle school, killing a math teacher before killing himself. Two victims from that attack were treated at Renown Regional.
The medical center also has treated victims of other recent tragedies, including a crash at a Reno air race in 2011 that killed 11 people and a shooting rampage at a Carson City restaurant the same year that killed three uniformed Nevada National Guard members.
Associated Press writers Sandra Chereb in Carson City and Ken Ritter in Las Vegas contributed to this report.