Armstrong spoke to this point in an interview for Writer's Digest. Ultimately the goal was to universalise the characters, allowing the reader to place themselves into the story and to view the other characters as being representative of general themes rather than specific people with their own individual goals, hope and desires.
"If the boy's age was not given the reader could become a part of the
story: 'The boy must be about my age.' Place and time kept vague, no
name or description of the boy. . . . And no names for the family.
With names they would have represented one family; without names they
became universal--representing all people who suffer privation and
injustice, but through love, self-respect, devotion, and desire for
improvement, make it in the world."
Sounder - 1970 review - The Newbery Project
You might want to note that one of the characters from the book (the boy, now named as Moses Waters) appears in a subsequent novel by the same author; Sour Land