The breaking of bread

The first disciples called the ceremony "the breaking of bread" (Luke 24:35; Acts 2:42; Acts 2:46; Acts 20:7; Acts 20:11).

This term is used by the Plymouth Brethren. -- Wikipedia

Lord's Supper

This is based on 1 Corinthians 11:20–21:

When you come together, it is not the Lord's Supper you eat, for as you eat, each of you goes ahead without waiting for anybody else. One remains hungry, another gets drunk.

Given its existence in the biblical text, "Lord's Supper" came into use after the Protestant Reformation and remains the predominant term among Evangelicals, such as Baptists and Pentecostals. They also refer to the observance as an ordinance rather than a sacrament. -- Wikipedia

Communion

The term Communion originate from the Protestant Reformation.

The term Communion is derived from Latin communio ("sharing in common"), translated from the Greek κοινωνία (koinōnía) in 1 Corinthians 10:16:

"The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?"

-- Wikipedia

Holy Communion

The Catholic Church, do not formally use this term for the Eucharist rite, but instead mean by it the act of partaking of the consecrated elements; they speak of receiving Holy Communion at Mass or outside of it, they also use the term First Communion when one receives the Eucharist for the first time. -- Wikipedia

Eucharist

The term eucharistia (thanksgiving) is that by which the rite is referred to in the Didache (a late 1st or early 2nd century document),51:437:207 and by Ignatius of Antioch (who died between 98 and 117) and by Justin Martyr (First Apology written between 155 and 157). Today, "the Eucharist" is the name still used by Eastern Orthodox, Oriental Orthodox, Catholics, Anglicans, Presbyterians, and Lutherans. -- Wikipedia

This is based on 1 Corinthians 11:23–24:

For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks (εὐχαριστήσας), he broke it, and said, "This is my body which is for you. Do this in remembrance of me".

The Sacrament

In the Church of Jesus Christ of Latter-day Saints the term "The Sacrament" is used of the rite. -- Wikipedia

Mass

The term "Mass" is used in the Catholic Church, the Lutheran churches (especially those of Sweden, Norway and Finland), and by some Anglicans. It derives from the Latin word missa, a dismissal: "Ite missa est," or "go, it is sent," the very last phrase of the service. That Latin word has come to imply "mission" as well because the congregation is sent out to serve Christ. -- Wikipedia

Divine Liturgy

The term Divine Liturgy (Greek: Θεία Λειτουργία) is used in Byzantine Rite traditions, whether in the Eastern Orthodox Church or among the Eastern Catholic Churches. -- Wikipedia

Divine Service

The term Divine Service (German: Gottesdienst) has often been used to refer to Christian worship more generally and is still used in Lutheran churches. -- Wikipedia

Holy Qurbana

Holy Qurbana is common in Syriac Christianity and Badarak in the Armenian Rite -- Wikipedia

Prosfora

In the Alexandrian Rite, the term Prosfora (from the Greek προσφορά) is common in Coptic Christianity -- Wikipedia

Keddase

The term Keddase is common in Ethiopian and Eritrean Christianity.