John uses the phrases “one whom Jesus loved” to refer to himself without using his own name.
One of his disciples, whom Jesus loved, was lying close to the breast of Jesus; (John 13:23)
So she ran, and went to Simon Peter and the other disciple, the one whom Jesus loved, and said to them, “They have taken the Lord out of the tomb, and we do not know where they have laid him.” (John 20:2)
That disciple whom Jesus loved said to Peter, “It is the Lord!” When Simon Peter heard that it was the Lord, he put on his clothes, for he was stripped for work, and sprang into the sea. (John 21:7)
John is referencing himself but it is also symbolic of you and I. We are all disciples whom Jesus loved. John also uses this type of phrase as a reference to others.
So the sisters sent to him, saying, "Lord, he whom you love is ill." (John 11:3)
Similarly, we are all ill and yet loved by Jesus the healer.
-Tim-