If you mean the literal name that you declared it with, that is generally compiled out unless you compiled with debugging symbols -g.
If you declared something on the stack, the machine code generally refers to the array elements as an offset from the frame pointer $ebp.
To answer your implied question, for an array on the stack, it does not exist. The machine code does not know what arr is. It only knows that there is a region of memory that you are addressing using offsets (indices in your code).
The question is more meaningful for an array on the heap, because now you have a pointer (which has its own address), and the memory which holds the actual array (which is on the heap, and stored inside the pointer).
Consider the following code.
char* arr = malloc(5);
Assuming you compiled with debug symbols, if you look at &arr inside gdb, you will see the address where the pointer arr is stored.
You can demonstrate the same thing if you create a separate pointer to an array on the stack.
char arr[10];
char* ptr = arr;
Here, you will see that ptr has separate storage (p &ptr), and holds the address of arr as its value, but &arr itself is equal to the address of its first element.