The code your wrote is wrong on a few levels. Your line

char *name[] = {"monkey", "pig", "goat", "dog", "cat"};

creates an array of char pointers, each pointing to a NULL-terminated string. So far, so good. However, your line

int *found = strstr (*name,"dog");

sets found to a pointer to the first occurrence of "dog" in *name = name[0] = "monkey". Besides not looking through the array name as you intend, you're also assigning the char * returned by strstr to an int *. Not good. Your next line

printf("Found at %i \n", found);

tries to print found, but the specifier requires an int and you're passing it found, an int *. These are all things to avoid, and I think a lot of this is undefined behavior.

What you want is a loop that uses strcmp, for example:

char *name[] = {"monkey", "pig", "goat", "dog", "cat"};
unsigned int numElements = sizeof(name)/sizeof(name[0]);
unsigned int i;
for(i = 0; i < numElements; ++i) {
    if (strcmp(name[i], "dog") == 0) {
        printf("Found at %u\n", i);
        break;
    }
}
if (i >= numElements) {
    printf("Not found\n");
}

Computing numElements in this way won't work if you pass the array into a function, so you'll have to explicitly pass the number of elements in that case.