The problem is you have a pointer that does not point to any actual data. Also name does not need to be a global variable. It can be within the scope of your main function.
You should probably use a string for this and you have already included its header so you could do this :
int main()
{
std::string name;
cout << "Hail adventurer!" << endl;
sleep(1.5);
cout << "What is your name?: ";
cin >> name;
cout << name << " ay?";
return 0;
}