Is “Eucharistic Minister” the correct title for a layperson who assists in distributing the Eucharist at Mass?
No, the title is not correct. Redemptionis Sacramentum states:
This function is to be understood strictly according to the name by which it is known, that is to say, that of extraordinary minister of Holy Communion, and not "special minister of holy Communion" nor "extraordinary minister of the Eucharist" nor "special minister of the Eucharist," by which names the meaning of this function is unnecessarily and improperly broadened. (RS 156)