The plate is usually called a “communion-plate” or “communion plate”.
From the General Instruction of the Roman Missal:
“287. If Communion from the chalice is carried out by intinction, each communicant, holding a Communion-plate under the mouth, approaches the Priest who holds a vessel with the sacred particles, with a minister standing at his side and holding the chalice.”
From Holy Communion and the Worship of the Eucharist Outside of Mass:
“19. When communion is given in a church or oratory, a corporal is to be placed on the altar, which is already covered with a cloth. A communion plate is to be used.”
The Latin word is patina. The sentence “A communion plate is to be used.” is a translation of “Patina adhibeatur.”
I believe that self intinction is permitted for bishops and priests, if they are concelebrants. But it is not permitted for deacons or lay people. This belief is based on the 1975 General Instruction of the Roman Missal, (as published in Documents of the Liturgy 1963 – 1979 by Liturgical Press, in 1982, n. 1596):
“206. If the concelebrants receive communion by intinction, the principal celebrant receives the body and blood of the Lord in the usual way, making sure that enough remains in the chalice for their communion. Then the deacon or one of the concelebrants arranges the paten with the eucharistic bread and the chalice conveniently in the center of the altar or at the right side on another corporal. The concelebrants approach the altar one by one, genuflect, and take a particle, dip part of it into the chalice, and, holding a paten under their chin, communicate. Afterward they return to their places as at the beginning of Mass.
The deacon receives communion also by intinction and to the concelebrant’s words: The body and blood of Christ, makes the response: Amen. At the altar the deacon drinks all that remains in the chalice, takes it to the side table and there he or the acolyte purifies and dries it, then arranges it in the usual way.”
Here I think “holding a paten under their chin” would be referring to a communion plate. But I do not have a copy of the Latin text with me to be sure that it has “patina”.
The 2004 Instruction Redemptionis Sacramentum has: “[104.] The communicant must not be permitted to intinct the host himself in the chalice, nor to receive the intincted host in the hand.”
The 1975 General Instruction of the Roman Missal described intinction by a priest on his own in 247. Two methods are described. Holding the paten and chalice in one hand. Having a small table with a cloth and corporal with the chalice or ciborium placed on it.
Continued below …
[Excerpts from the English translation of The Roman Missal © 2010 International Commission on English in the Liturgy Corporation, ICEL. Excerpts from the English translation of The Roman Missal © 1975, ICEL. Excerpts from the English translation of Holy Communion and the Worship of the Eucharist Outside of Mass © 1974, ICEL. All rights reserved.]