It's usually the airport authority which sends the information to ATC for transmission to pilots.
What happens prior to that can be quite complex. An airline will operate from a particular terminal but stand allocation by the airport authority within that terminal will depend on a number of factors - airline, aircraft type and size, jetty serviceability, whether domestic or international, etc, etc. If a large terminal is for the exclusive use of one airline, that airline will decide parking arrangements within the terminal in liaison with the airport authority.
That's very basic, but a lot more is involved.