Why did DuBois call his book The Souls of Black Folk?

W.E.B. Du Bois titled his book The Souls of Black Folks because it discusses issues that black people face, how they see themselves, and his hope that they will be judged by their souls rather than their race. Each of these concepts tie in to the deeper issue of how black people see themselves and experience life in America. 
Du Bois opens his book by explaining at least part of its purpose, saying: "Herein lie buried many things which if read with patience may show the strange meaning of being black here at the dawning of the Twentieth Century." He goes on to explain the issues facing black people in post-Civil War America. Du Bois discusses the right to vote, the lack of equality, and the desire for education.
Du Bois is in favor of education, not only because it will help create leaders and people who can guide the black community, but also because it will feed their souls. He writes:

The industrial school springing to notice in this decade, but coming to full recognition in the decade beginning with 1895, was the proffered answer to this combined educational and economic crisis, and an answer of singular wisdom and timeliness. From the very first in nearly all the schools some attention had been given to training in handiwork, but now was this training first raised to a dignity that brought it in direct touch with the South's magnificent industrial development, and given an emphasis which reminded black folk that before the Temple of Knowledge swing the Gates of Toil.
Yet after all they are but gates, and when turning our eyes from the temporary and the contingent in the Negro problem to the broader question of the permanent uplifting and civilization of black men in America, we have a right to inquire, as this enthusiasm for material advancement mounts to its height, if after all the industrial school is the final and sufficient answer in the training of the Negro race; and to ask gently, but in all sincerity, the ever-recurring query of the ages, Is not life more than meat, and the body more than raiment? 

It's essential to him that black people not only have opportunities in society, but also that they have the opportunity to understand who they are outside of the roles and prejudices thrust upon them by white Americans. Only having technical training for jobs won't help fulfill the needs of their souls. 
Du Bois also addresses how black people see themselves. An important concept in the book is that of the veil, which represents the barrier between black people and the rest of America. The veil is what keeps white people from seeing black people as truly equal and recognizing the problems of justice and equality in society. More importantly, perhaps, the veil prevents black people from seeing themselves outside the stigma placed on them by white people. As Du Bois says, "I was different from the others; or like, mayhap, in heart and life and longing, but shut out from their world by a vast veil." 
He says that black people experience a double-consciousness where they judge themselves through the eyes of a world that has contempt and pity for them. He says, "One ever feels his twoness,—an American, a Negro; two souls, two thoughts, two unreconciled strivings; two warring ideals in one dark body, whose dogged strength alone keeps it from being torn asunder." This idea of two souls contributed to the title of Du Bois's book. Throughout it, he explores how black people have progressed -- and can progress further -- because of and in spite of this double-consciousness and the veil. 
He explains that part of the being a black person in America is the desire to become a single person rather than these two parts that aren't entirely merged. Both parts of the person -- the American and the African -- have something to offer him. Unfortunately, he explains, being both causes him to be "cursed and spit upon by his fellows" and keeps him from equal opportunity. 
One personal tale that Du Bois shares is that of his son, who died very young. Du Bois says of him that "he loved the white matron, he loved his black nurse; and in his little world walked souls alone, uncolored and unclothed." A child doesn't see people as defined by their race because he isn't old enough yet to recognize the prejudices that people learn; no one is born with them. Du Bois thinks that maybe his son is more free for having died instead of living longer and seeing the ugliness in the world. He writes:

All that day and all that night there sat an awful gladness in my heart,—nay, blame me not if I see the world thus darkly through the Veil,—and my soul whispers ever to me saying, "Not dead, not dead, but escaped; not bond, but free." No bitter meanness now shall sicken his baby heart till it die a living death, no taunt shall madden his happy boyhood. Fool that I was to think or wish that this little soul should grow choked and deformed within the Veil! I might have known that yonder deep unworldly look that ever and anon floated past his eyes was peering far beyond this narrow Now. In the poise of his little curl-crowned head did there not sit all that wild pride of being which his father had hardly crushed in his own heart? For what, forsooth, shall a Negro want with pride amid the studied humiliations of fifty million fellows? Well sped, my boy, before the world had dubbed your ambition insolence, had held your ideals unattainable, and taught you to cringe and bow. Better far this nameless void that stops my life than a sea of sorrow for you.

Though his physical body has died, his soul has escaped the sorrow and torture that black people in America face as they grow older and begin to understand the concept of the veil. His son was too young to understand the problems that come with being black in America and escaped the hardships he would have faced. 
In the end, Du Bois shares his hope that "that sometime, somewhere, men will judge men by their souls and not by their skins." The souls of black people -- as Du Bois has shown throughout his text -- are weighed down by the color line that divides them from the rest of America and the resulting mistreatment. They are denied justice and equal opportunity because of their skin; that doesn't have to last forever, though. This, perhaps, is the driving force behind the title of his book -- that things can get better and people can be judged for who they are, rather than how they look. 
https://docsouth.unc.edu/church/duboissouls/bio.html