Simply use strcmp !

I have modified the code, and now it has two options, either you can sort by grades with BubbleSortGRADE, or sort by names with BubbleSortNAME.

The code has a function MakeUppercase that converts strings to uppercase before comparison, so that letters like 'a' and 'A' are treated alike while sorting.

Code: C
#include <stdio.h>
#include <string.h>

#define UpperLimit 500

struct Student
{
      char NAME [50];
      short GRADE;
} StudentData [UpperLimit];

void BubbleSortGRADE(struct Student Array[], int Size)
{
      int i, j;
      struct Student Temp;
      for(j = 0; j < Size; ++j)
      {
        for(i = 0; i < Size - 1; ++i)
        {
          if(Array[i].GRADE > Array[i+1].GRADE)
          {
             Temp = Array[i];
             Array[i] = Array[i+1];
             Array[i+1] = Temp;
          }
        }
      }
}

void MakeUpperCase(char *MyString)
{
      int i, j = strlen(MyString);
      for(i = 0; i < j; ++i)
        MyString[i] = toupper(MyString[i]);
}

void BubbleSortNAME(struct Student Array[], int Size)
{
      int i, j;
      struct Student Temp;
      char Name_A[50], Name_B[50];
      for(j = 0; j < Size; ++j)
      {
        for(i = 0; i < Size - 1; ++i)
        {
          strcpy(Name_A, Array[i].NAME);
          MakeUpperCase(Name_A);
          strcpy(Name_B, Array[i+1].NAME);
          MakeUpperCase(Name_B);
          if( strcmp(Name_A, Name_B) > 0 )
          {
             Temp = Array[i];
             Array[i] = Array[i+1];
             Array[i+1] = Temp;
          }
        }
      }
}

void main(void)
{
      int i, Index = 0;
      FILE* MyFile = fopen("C:\\Test.txt", "r");
        while( ! feof(MyFile) )
        {
          fscanf(MyFile, "%s %d", StudentData[Index].NAME, &StudentData[Index].GRADE);
          Index++;
        }
      fclose(MyFile);

      BubbleSortNAME(StudentData, Index);

      MyFile = fopen("C:\\Sorted.txt", "w");
        for(i = 0; i < Index; ++i)
          fprintf(MyFile, "%s %d\n", StudentData[i].NAME, StudentData[i].GRADE);
      fclose(MyFile);
}

NOTE : The questions that you are asking are pretty simple. If you are unable to answer these yourself, you are really weak in C/C++. I am not advising you, rather it's just my suggestion as a well-wisher that you try to write some code yourself. Copying the code from someone else and submitting it as a project would do no good. Just my 2 cents ..