Thanks, 999.
In case the link gets broken, that website is "Hymns And Carols Of Christmas: What You Gonna Call Your Pretty Little Baby?

And it is an African-American spiritual, with several different versions and titles:

Mary, What You Gonna Name that Pretty Little Baby?
Mary, Mary (What You Gonna Name That Baby?)
Glory To That Newborn King

Various versions have been recorded by Harry Belafonte, Joan Baez, Carolyn Hester, Peggy Seeger and John Jacob Niles

The sheet music for several of these versions is available on-line, e.g.: http://www.musicnotes.com and www.sheetmusicplus.com.