Is it sufficient to invoke blessings upon the Prophet by saying, "May the peace and blessings of Allah be upon him," and is it obligatory to invoke blessings upon him when his name is repeated in writing?

There is no impediment to sufficing with the phrase "alaihi al-salat wa al-salam" (upon him be peace and blessings) when mentioning the Prophet, may Allah bless him and grant him peace, for it is like saying "salla Allahu alaihi wa sallam" (may Allah bless him and grant him peace), and both are supplications. Both phrasings have been reported in the speech of the Companions, such as the sayings of Uthman, Ibn Abbas, and Umar. Prayers are invoked upon the Prophet, may Allah bless him and grant him peace, whenever his name is read or heard.