Behold! The Lamb of God who takes away the sin of the world!
Scripture behind the name
In the Old Testament, the Passover lamb was connected with deliverance. Israel was rescued through the blood of the lamb and the mercy of God. In the New Testament, Christ is revealed as the true Passover and the Lamb who takes away the sin of the world. The Coptic Liturgy receives that biblical language and places it at the center of the Eucharistic offering.
Calling the chosen offering the Lamb therefore teaches the faithful how to understand the whole service. The Eucharist is thanksgiving, but it is thanksgiving through the sacrifice of Christ. It is a meal, but it is the meal of the sacrificed and risen Lord. It is Communion, but Communion in the One who gives Himself.
How this connects to Communion
The Lamb is offered, prayed over, consecrated, broken in the Fraction, and given to the faithful in Holy Communion. The same word follows the movement from the beginning of the Liturgy to Distribution. What is chosen at the Offering of the Lamb becomes, by the work of the Holy Spirit, the holy Body of Christ given for salvation, remission of sins, and eternal life.
When the Church says Lamb, she is not giving a decorative name to bread. She is confessing Christ crucified and risen, present in the Eucharistic mystery, and offered to the faithful as life.