I will offer explanations of two of the names, leaving the others to those who are more qualified.
a) Mr. Gradgrind: He is the headmaster of the school in Hard Times. He is interested in cold facts and figures; emotions and artistic expressions are out of place in his school. He teaches his students that it is improper to put a flowered pattern on a carpet -- because it would not make sense to step on the flowers!
Mr. Gradgrind wants to grind out facts and fact-loaded students the way a mill grinds grain into flour.
I'm not sure what "grad," the first part of his name, refers to. Perhaps it is a variant of the word "grade," indicating that Mr. Gradgrind is not interested in his students as human beings, but only as vehicles for producing grades.
b) Mr. McChoakumchild is a teacher in Mr. Gradgrind's school. He is, for Mr. Gradgrind, a model teacher. He pours into his students' heads facts, facts, and more facts, with no consideration for their development as human beings.
It is quite obvious that McChoakumchild's name indicates that he "chokes" the children rather than helping them grow and learn.
The beginning of his name, "Mc," is a common prefix to Scottish names. It has been suggested that Dickens may have been thinking of two contemporary Scotsmen, both named McCulloch. J.M.M. M’Culloch, was a headmaster in Edinburgh, Scotland who was known for his practical and dry textbooks; J. R. McCulloch, was a well-known political economist and statistician (see second link below).