Neither of the local Melkite parishes used the communicant’s name when I received from them. (The translation on the Melkite Eparchy of Newton has the communicant’s name being used.) Our Russian parish does commune with names-- it’s in the text of the OCA which is what we use. It’s also in The Byzantine Luturgy: A New English Translation… Third Revised Edition put out by the Russian Center at Fordam University in 1955 which was in use in the past in my parish when we switched from Slavonic. “The servant/handmaid of God, N, receives the precious and Holy Body and Blood…” The Ruthenian priest here communes using the name of the communicant. In the Melkite parishes and the Ruthenian those priests knew me so I don’t know what would have happened were I a stranger approaching for Holy Eucharist.
I also recall a conversation I had with some Orthodox, who expressed a bit of shock that Catholics follow such a policy, since Anglicans, Lutherans, Methodists, etc could be getting in line. (I don’t recall too many details of the conversation, as it was some years ago.)
They get in line at times in the Latin Church, as do Catholics who are not “properly disposed”.
We have visitors at most Liturgies in my ECC. Typically some do not go up for Eucharist for whatever reason. Most of our visitors are Latin Catholics and they usually approach one of us and say something about it being their first time. We do get Orthodox visitors, and typically they don’t go up, tho at least one does when she visits. I think if someone presents for Eucharist in my parish the priest will commune them, similar to the Latin Church. Sometimes we have a large group of visitors and at those times our priest tends to say something before beginning distribution about how to receive if they are going to receive.
A few days ago I was at a funeral in a Latin parish. I was seated very near the Extraordinary Minister of Holy Communion who had the Precious Blood. One person who approached and took the cup seemed clearly unfamiliar with what to do. Unfortunately the priest’s comment at the time for people to approach made no mention of Eucharist being sorely for Catholics, properly prepared to receive Him. EMsHC are trained that it is their duty to safe guard the Eucharist so I felt this EMHC was in a very odd position when the priest had made not effort to instruct the many visitors there about who should and should not approach.