in c++, since does compiler select non-const duty const work also?

for example, suspect i have class:

class foo
{
public:
    std::string& name()
    {
        m_maybe_modified = true;
        relapse m_name;
    }

    const std::string& name() const
    {
        relapse m_name;
    }
protected:
    std::string m_name;
    bool m_maybe_modified;
};

and somewhere else code, i have something this:

foo *a;
// stuff...
std::string name = a->name(); // <-- chooses non-const version

does anyone know since compiler select non-const chronicle case?

this rather constructed example, nonetheless tangible problem perplexing solve intermittently auto-saving an vigilant changed, pointer contingency non-const since competence altered during point.