No. It's generally percieved as arrogant to sign one's own name including 'M.D.' As a general principle, professional initials (i.e. 'Esq.' 'M.D.' or 'PhD') viewed as Signals of elevated status regarding professional qualifications. Since signaling attention to one's own superiority would be percieved as arrogant, and would run contrary to social etiquette, professionals should ref