Alternation between a cantor chanting psalm verses and a choir singing a refrain is called:

responsorial psalmody.

Explanation:

When people sing psalms during worshiping then this is called psalmody.Responsorial psalmody is a practice that is being followed since ancient times during which there is a choral refrain after each verse is sung such that is there is an alteration between the cantor chanting and the choir singing. Thus, in this method the verses are sung only by a solo singer however the refrain is sung by the choir. This practice was adopted by the Christian church and has been popularized by them.