No matter what you think, there is no such thing as a lay "Eucharistic Minister"

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Many parishes have commissioned "Eucharistic Ministers" in error to assist their priests when the number of communicants is large and would take too long for one or two ordained ministers carry out the responsibility.

You see, the priest is the "Eucharistic Minister" and priests and deacons are the "Ordinary Ministers of Holy Communion." The parish may not commission "Eucharistic Ministers" because that function is reserved for the priests who act "in persona Christi" at the Consecration in the Mass.

If additional people are needed, male or female, they are to be called "Extraordinary Ministers of Holy Communion." See the U.S. Conference of Catholic Bishops' Committee on the Liturgy regulations here.