Tolkien named the great eagle that rescued Gandalf from Isengard Gwaihir.
In The Lord of the Rings, Gwaihir is the Lord of the Eagles of the Misty Mountains. He rescues Gandalf after the wizard is imprisoned by Saruman at the summit of Orthanc. Gwaihir later carries Gandalf away after the battle with the Balrog on the peak of Zirakzigil.
Gwaihir also helps at key moments near the end of the story, including the rescue of Frodo and Sam after the destruction of the One Ring. His interventions are important, but the Eagles are not presented as a simple alternative transport service for the entire quest. Tolkien’s story gives narrative and strategic reasons why they cannot simply fly the Ring to Mordor.
Thorondor is a different and earlier Eagle, associated mainly with the First Age. Landroval and Meneldor are also named Eagles, which makes the names easy to confuse.