CCC 478 Jesus knew and loved us each and all during his life, his agony and his Passion, and gave himself up for each one of us: “The Son of God. .. loved me and gave himself for me.”1 He has loved us all with a human heart. For this reason, the Sacred Heart of Jesus, pierced by our sins and for our salvation,2 “is quite rightly considered the chief sign and symbol of that. .. love with which the divine Redeemer continually loves the eternal Father and all human beings” without exception.3

CCC 616 It is love “to the end”4 that confers on Christ’s sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life.5 Now “the love of Christ controls us, because we are convinced that one has died for all; therefore all have died.”6 No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. The existence in Christ of the divine person of the Son, who at once surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.

CCC 1380 It is highly fitting that Christ should have wanted to remain present to his Church in this unique way. Since Christ was about to take his departure from his own in his visible form, he wanted to give us his sacramental presence; since he was about to offer himself on the cross to save us, he wanted us to have the memorial of the love with which he loved us “to the end,”7 even to the giving of his life. In his Eucharistic presence he remains mysteriously in our midst as the one who loved us and gave himself up for us,8 and he remains under signs that express and communicate this love:
The Church and the world have a great need for Eucharistic worship. Jesus awaits us in this sacrament of love. Let us not refuse the time to go to meet him in adoration, in contemplation full of faith, and open to making amends for the serious offenses and crimes of the world. Let our adoration never cease.9

CCC 2666 But the one name that contains everything is the one that the Son of God received in his incarnation: JESUS. The divine name may not be spoken by human lips, but by assuming our humanity The Word of God hands it over to us and we can invoke it: “Jesus,” “YHWH saves.”10 The name “Jesus” contains all: God and man and the whole economy of creation and salvation. To pray “Jesus” is to invoke him and to call him within us. His name is the only one that contains the presence it signifies. Jesus is the Risen One, and whoever invokes the name of Jesus is welcoming the Son of God who loved him and who gave himself up for him.11

1 Cal 2:20.
2 Cf. Jn 19:34.
3 Pius XII, Enc. Haurietis aquas (1956): DS 3924; cf. DS 3812.
4 Jn 13:1.
5 Cf. Gal 2:20; Eph 5:2, 25.
6 2 Cor 5:14.
7 Jn 13:1.
8 Cf. Gal 2:20.
9 John Paul II, Dominicae cenae, 3.
10 Cf. Ex 3:14; 33: 19-23; Mt 1:21.
11 Rom 10:13; Acts 2:21; 3:15-16; Gal 2:20.