you will have to actually read all the lines sequentially from beginning of the file to end of the file. Since the name appears consistently on every other line, that is all you have to keep in the program -- you can just toss the others into the bit bucket.
use fopen() to open the file in text mode, and fgets() to read each line. I suspect the function should copy the names into some sort of character array so that the calling function can use them for something. Generally you would want to use a linked list, but that's probably beyone the scope of your assignment. Just have the calling function create a 2d array and pass it to the function that reads the array.
Code:
void read_names(char names[10][])
{
// blabla
}
int main()
{
char names[10][40];
read_names(names);
}