Returning a const reference to an object instead of a copy

Whilst refactoring some code I came across some getter methods that returns a std::string. Something like this for example:

class foo
{
private:
    std::string name_;
public:
    std::string name()
    {
        return name_;
    }
};

Surely the getter would be better returning a const std::string&? The current method is returning a copy which isn't as efficient. Would returning a const reference instead cause any problems?