Is there going to be like a new operator called Airport Express for the train to the airport?

Yes

Btw guys, The airport link will go to several places, which include Chinchester city, Whitecoast central, Mirna town, Redborough, and Rosewells. No service from NC bcz its close to the airport and there is also going to be a shuttle that runs with a class 185 triple unit that has 9 coaches. (shuttle is that red line.)