are there also companies that rent appartment, if so how this is called?
Polish name for it is "pośrednictwo wynajmu" - rental agency.
I'm really curious if there is a way to rent some appartment from a company instead of landlord.
It depends from a landlord (mostly an owner) if he needs to order such service, eg. he have no time to deal with it alone, and has multiple properties. So not all apartments for rent have assigned agents. There's no choice for you I'm afraid.