It should be noted that Peterson’s lyrics (following the lead of the Good News Bible and the New Living Translation) substitutes “Jehoiachin” for “Jeconiah,” the form of the name actually given in St Matthew 1:11-12. Eugene Nida explains,
“Strange proper names [....] pose problems for both readers and translators, especially when the same object or person may be referred to by more than one name. [....] [T]he ordinary reader would not know that the names ‘Jeconiah’ (Jer. 24:1) and ‘Coniah’ (Jer. 37:1) are variations on the name of the king of Judah usually called ‘Jehoiachin.’ [....] As indicated in the preface of the Good News Bible, its translators have chosen to use consistently that form of a particular name which is most widely used and known.”1
Also, following all major translations since the English Revised Version of 1881, Peterson’s lyrics give the names in the genealogy as though transliterated directly from Hebrew. The King James Version and Douay-Rheims Bible alone transliterate the names according to what the Greek text has. The chief differences are: “Perez” for “Phares” (v. 3); “Rehoboam” for “Roboam” (v. 7); “Jehoshaphat” for “Josaphat” (v. 8); and “Shealtiel” for “Salathiel” (v. 12). Sometimes “Ram” is given for “Aram” in vv. 3-4.
As for “Mary, Mother of Christ” at the end of the song, while I would have preferred “Mary, Mother of Jesus the Christ” (which would more closely parallel v. 16), I’m sure that Mr Peterson did this quite innocently and in no way wishes to advance an heretical Nestorian Christology!
1 Eugene A. Nida, Good News for Everyone: How to Use the Good News Bible (Waco: Word, 1997), pages 83-84.