A dangling pointer is a pointer that points to invalid data or to data which is not valid anymore, for example:

CopyClass *object = new Class();
Class *object2 = object;

delete object;
object = nullptr;
// now object2 points to something which is not valid anymore

This can occur even in stack allocated objects:

CopyObject *method() {
  Object object;
  return &object;
}

Object *object2 = method();
// object2 points to an object which has been removed from stack after exiting the function

The pointer returned by c_str may become invalid if the string is modified afterwards or destroyed. In your example you don't seem to modify it, but since it's not clear what you are going to do with const char *name it's impossible to know it your code is inherently safe or not.

For example, if you store the pointer somewhere and then the corresponding string is destroyed, the pointer becomes invalid. If you use const char *name just in the scope of new_foo (for example, for printing purposes) then the pointer will remain valid.