Answer:
The method written in Java is as follows:
public static void classAttendance(){
    Scanner input = new Scanner(System.in);
    String[][] names = new String[10][10];
    for(int i =0;i<10;i++){
     for(int j =0;j<10;j++){
        System.out.print("Student Name: "+(i+1)+" , "+(j+1)+": ");
        names[i][j] = input.nextLine();         
     }   
    }
}
Explanation:
This defines the classAttendance() method
public static void classAttendance(){
    Scanner input = new Scanner(System.in);
This declares the 2D array of 10 by 10 dimension as string
    String[][] names = new String[10][10];
This iterates through the rows of the array
    for(int i =0;i<10;i++){
This iterates through the columns of the array
     for(int j =0;j<10;j++){
This prompts user for student name
        System.out.print("Student Name: "+(i+1)+" , "+(j+1)+": ");
This gets the student name from the user
        names[i][j] = input.nextLine();         
     }   
    }
The method ends here
}
<em>See attachment for complete program that include main method</em>