In J.R.R. Tolkien’s legendarium, the great eagle who rescues Frodo and Sam is Gwaihir.
Gwaihir is the Lord of the Eagles in the Third Age. He helps Gandalf on several occasions and leads the rescue of Frodo and Sam from the slopes of Mount Doom after the One Ring is destroyed. The rescue takes place after the eruption and collapse of Orodruin, when the two Hobbits are stranded in the devastated land of Mordor.
Gwaihir also carries Gandalf away after the wizard’s battle with the Balrog on the peak of Zirakzigil. Later, he and other Eagles assist in the Battle of the Five Armies and the Battle of the Morannon.
Tolkien’s eagle names can be confusing. Thorondor is the greatest of the Eagles in the First Age, while Landroval is another important eagle of the Third Age. The Eagles are powerful independent beings, not ordinary birds that characters can summon whenever convenient.