The Gospel according to John lacks the account at the Last Supper; there is no "Take, eat; this is My body..." But commentators note while lacking those words, John includes things which show a greater interest in the eucharist. C.K. Barrett says (my emphasis added):
The reason of John's omission of the significant words and action of Jesus at the last supper is discussed below (p. 71), but what is said there must be anticipated here because it points the way to an understanding of John's omission of the other events which have been mentioned. It is certain that John was more, rather than less, interested in the eucharist that the synoptics; he gives indirect teaching on the subject at some length. But because he was concerned to root the sacrament as observed by the Church in the total sacramental fact of the incarnation, he was unwilling to attach it to a particular moment and a particular action.1
The sacraments, then, so far as the appear in John, are means by which Christians are incorporated into the saving work of Christ, sharing thus in the descent of the Redeemer to an obedient death, and in his ascent through death to the glory he enjoyed with the Father before the creation. There is thus a close relation between the Johannine teaching and Paul's baptismal doctrine of crucifixion, burial, and resurrection with Christ, and his eucharistic doctrine of a rite based upon the proclamation of the Lord's death and continued in hope of his return in glory, though there is no literary ground for supposing that John had heard of Paul's terminology.2 3
Commentating on the Bread of Life Discourse Barrett says:
John is less ready than some of his commentators to argue about the eucharist; he assumes it, and knows that his readers will assume it, while he also knows that except in the context of the fulfillment of God's purposes in the life, death, and resurrection of Jesus it is a meaningless ceremony. The realization of eschatology and the consequent gift of life by the death of Jesus, are central themes of this discourse as of the whole gospel.4
The main theme of the Prologue5 is the necessity of belief in His name and receiving Him in order to have the right to becoming a child of God:
But to all who did receive (ἔλαβον) him, who believed in his name, he gave the right to become children of God (John 1:12) [ESV]
John includes the necessity to "receive" λαμβάνω after believing in His name. In other words, it is not simply a matter of belief or to receive: both must be present.
John's "receive" is how Jesus instructed those at the Last Supper:
Now as they were eating, Jesus took bread, and after blessing it broke it and gave it to the disciples, and said, “Take (Λάβετε), eat; this is my body.” (Matthew 26:26)
And as they were eating, he took bread, and after blessing it broke it and gave it to them, and said, “Take (Λάβετε); this is my body.” (Mark 14:22)
Should λαμβάνω in John 1:12 be seen in light of the Last Supper? In other words, has John written to correct those who thought they could eat without believing, as Judas did?6
Notes:
1. C.K. Barret, The Gospel According to St. John, S.P.C.K, 1962, p. 41
2. Ibid., p. 71
3. Barret also says "The reader of the New Testament cannot fail to be impressed by the considerable measure of agreement between John and Paul in their presentation of Christian theology." (p. 45) On the topic of the eucharist, Jeremias, citing J.H. Bernard, shows John 6:51c follows 1 Corinthians 11:24b stating, "John has only expanded it paraphrastically at the beginning and at the end." [Joachim Jeremias, The Eucharistic Words of Jesus, Translated by Norman Perrin, SCM Press Ltd, Trinity Press International, 1966, p. 107-108]
4. Ibid., p. 236
5. Brad McCoy, "Chiasmus: An Important Structural Device Commonly Found in Biblical Literature", [Chafer Theological Seminary], p. 29 [Adapted from M.É. Boismard, Le Prologue de Saint Jean, Lectio Divina, vol. 11 (Paris: du Cerf, 1953), 107]
6. At the time of writing, eating food sacrificed to idols or to false gods was a common occurrence and an issue for the Church. So the condition is not simply one of belief on the part of the participant. (No doubt those who engaged in the pagan feasts believed there was some benefit.) The issue is belief in Jesus and participation in the meal He instituted.