John Chrysostom

He however, to signify that He is far from coming to the passion against His will, both rebuked Peter, and called him Satan. Let them hear, as many as are ashamed of the suffering of the cross of Christ. For if the chief apostle, even before he had learnt all distinctly, was called Satan for feeling this, what excuse can they have, who after so abundant proof deny His economy? …

Homily on the Gospel of Matthew 54 ↗

Theophylact of Ohrid

But He turned and said unto Peter, Get thee behind Me, Satan: thou art an offense unto Me: for thou savourest not the things that be of God, but those that be of man. When Peter spoke rightly, Christ called him blessed, but when he was irrationally dismayed, and did not want Him to suffer, then Christ rebuked him and said, "Get thee behind Me, Satan." "Satan" means "the adversary." "Get thee behind Me," that is, do not oppose Me, but follow My will. He calls Peter this because Satan, too, did not wish Christ to suffer. …

Commentary on Matthew ↗

Bernard of Clairvaux

When he was speaking about his approaching death, Peter who loved him so dearly, tried to stand in the way. When, as you remember, he rebuked him, what was it but his imprudence that he was correcting? Finally what did he mean in saying: "You do not mind the things of God," except: you do not love wisely, you are following your human feeling in opposition to the divine plan. He even called him Satan because although it was in ignorance, he was impeding salvation in trying to prevent the Savior's death.

Sermons on the Song of Songs, Sermon 20 ↗