What is the operational convention for titling a crew member launched aboard a Russian Soyuz spacecraft?

They are generally referred to as a cosmonaut, regardless of their nationality

An operational convention exists layering on top of the primary training definition regarding the launch vehicle. Standard operating procedure dictates that if a crew member, regardless of their home agency's designation (astronaut or cosmonaut), launches aboard a Russian Soyuz spacecraft, they are generally referred to as a cosmonaut for the duration of that mission or operational phase. This contrasts with the rule for Western vehicles like the NASA Crew Dragon, where a traveler would be referred to as an astronaut. Although the designation ultimately sticks to the person based on their primary training, this operational naming convention can temporarily blur the lines, especially during cooperative missions like those involving the Shuttle-Mir program or the ISS.