This is the 4937th most frequent Russian word.
компаниями
"Компаниями" means "by companies" (instrumental plural of "компания").
In this sentence, 'компаниями' is the instrumental plural form of 'компания', meaning 'companies'. It is used to indicate the entities with which the subject collaborates.
Мы сотрудничаем с различными компаниями.
We collaborate with various companies.
Here, 'компаниями' is again the instrumental plural of 'компания'. It specifies the entities that performed the action of organizing the training.
Тренинг был организован международными компаниями.
The training was organized by international companies.
Once more, 'компаниями' appears in the instrumental plural form, used to describe the entities she collaborates with in her work.