Why didn't the author give Hally's parents names??
I believe that Hally's parents are unnamed because they are to represent the average white family in pre-Apartheid society. They also represent the strong force that culture can play in a person's life.
Sam and Willy are much more important to Hally in his day to day life than his parents. The fact that the two servants Sam and Willy are named gives them an importance. Usually, the names of the servants aren't important. That they are named and given a personality and role in Hally's life is significant. However, Hally in some ways succumbs to his 'culture' as represented by his nameless parents and adopts an apartheid stance.
The word "father" connotes many warm feelings in our culture, but the word also has come to signify above all else "authority," and it is the issue of authority, whether by a parent or by of race, that the play calls into question. Indeed, the relationship between Sam and Hally at the beginning of the play is one of harmony and respect, symbolized by the possibilities of the ballroom dancing, where people must move together, aware of each other, to achieve grace and beauty. The word "father" as well as the character himself destroys this. In some ways, the use of this word shows the relationship between racism and sexism, in the form of patriarchy, in the culture:both are about power.