Basil Onuferko, 26, had been working for Phoenix company TransPac Aviation Academy, which released a statement Friday about the crash.
Another flight instructor for the company also died.
"We extend our deepest condolences to the family, friends and fellow colleagues of the two instructors that were lost today," said TransPac CEO Stephen Goddard.
"The individuals involved were deeply connected here at TransPac and their loss is felt by all of us. The entire extended TransPac community, including our alumni, is in shock and mourning for the loss of both of these two good men."
Onuferko 'well-loved and respected'
The U.S. Federal Aviation Administration and National Transportation Safety Board are investigating, according to the statement.
The company said it can't comment on possible causes of the crash while the investigation is underway.
The statement did not include the names of the two men but, in Ottawa, the interim director of Saint Paul University's Metropolitan Andrey Sheptytsky Institute of Eastern Christian Studies posted a blog about Onuferko's death.
"Basil was well-loved and respected in the Ottawa community as was his family," Alexander Laschuk wrote.
Onuferko's father, Rev. Andriy Onuferko, is the Holy Spirit Ukrainian Catholic Seminary's spiritual director, according to its website. His mother, Marijka Onuferko, works as an administrative assistant at the seminary, it notes.
"For anyone who knew Basil, his smile was a source of great joy and his self-giving brightened the lives of all those he met," Laschuk wrote. "As funeral details are made available, they will be shared."
Phoenix police Sgt. Bill Linball said the two planes crashed just after 10 a.m. Friday.
KNXV-TV, the ABC News affiliate in Phoenix, reported Friday the TransPac plane was a Piper Archer. The flight school's website says it has a fleet of 40 Piper Archers.