"Progress" is used as the name of a Russian space research facility and factory (the Progress Rocket Space Centre), and also as a spacecraft that delivers cargo to space stations (Progress spacecraft). Was one of these named after the other? (It is not clear from the Wikipedia articles.)
Following the trail back in time, Progress Rocket Space Centre -> TsSKB-Progress -> Progress plant, named by the Ministry of General Machine-building in 1965.
As that's before the spacecraft (programme initiated in 1973), the centre is at least not named after it.
Though the word "progress" is pretty generic, both the plant and the program were in the same branch of the Soviet design bureau hierarchy, so I can sadly not rule out that the spacecraft was named after the plant.