In the example given in the talk, there are two overloads of getName() given.
One with the && and the other with the const& qualifiers.
Without the & after the const, the function const std::string& getName() const cannot be overloaded with the overload for rvalues string Customer::getName() &&. 
You would then have to remove the rvalue overload from the code completely if you want it to work.
Since ref qualified member functions were added only in C++11 (making the getter for rvalues possible), the change from const std::string& getName() const to const std::string& getName() const& was needed to make both overloads possible.
The C++17 standard draft n4659 states :
16.1 Overloadable declarations [over.load]
  ...  
2 Certain function declarations cannot be overloaded:
  ...
(2.3) — Member function declarations with the same name and the same parameter-type-list as well as member function template declarations with the same name, the same parameter-type-list, and the same template parameter lists cannot be overloaded if any of them, but not all, have a ref-qualifier.
Since there is one overload of getName() with a ref-qualifier (&&), the other one also should have the ref qualifier. This is why const& is required.