Can the words of the Lamb of God be altered?

Authoritative: YES

It is not infrequent in Catholic parishes to hear the words of the Agnus Dei altered so that other names of our Lord are inserted in place of "Lamb of God" (Prince of Peace, Bread of Life, etc.).

Are these alterations authorized?

The alteration of these phrases in the Agnus Dei (called "tropes"), though perhaps of innocent intention, is not permissible. The Agnus Dei is not a hymn, but part of the Canon of the Mass, and as such, its prayers are fixed by the Church's tradition.

As of September 12, 2012, the 2007 document that sets the norms for liturgical music in the United States (Sing to the Lord: Music in Divine Worship) was amended to specifically prohibit this practice. The pertinent quote comes from section 188. The amended section states:

"188. The supplicatory chant Agnus Dei accompanies the Fraction Rite. It is, "as a rule, sung by the choir or cantor with the congregation responding; or it is, at least, recited aloud. This invocation accompanies the fraction and, for this reason, may be repeated as many times as necessary until the rite has reached its conclusion, the last time ending woth the word dona nobis pacem (grant us peace)" (GIRM, no. 83). The Agnus Dei should not be prolonged unnecessarily (see GIRM, no. 83) nor may other texts be added to this chant."

This change was not just done unilaterally by the USCCB but was requested by the Congregation for Divine Worship, so this comes straight from the Vatican and has the weight and authority of the CDW behind it. Alterations of the text of the Agnus Dei are thus not permissible, not should the Agnus Dei be prolonged unnecessarily.