In American English I think we'd usually phrase it differently. Imagine you are flying to IAD, with a stop in ORD. You could naturally phrase this: "I'm flying to IAD with a connection in ORD." "I have a connecting flight in Chicago." Referring to the airport itself doesn't come up much, but "connecting airport" seems more natural than "transferring airport" to me.

I would probably call it a connecting airport, but I would understand either phrase.

you mean the flight,it's called a transit flight

We usually say there is a layover at XYZ (airport), but it is referring to the time waiting between flights. Or "there is a 3 hour layover at XYZ". We could also say we need to transfer at XYZ.

Thank you, Joe. Are you saying that "layover" can also refer to some hours of stop halfway for unexpected reasons?