Is it permissible to forbid someone on Facebook who is cursing those who do not write one of the Beautiful Names of Allah, by saying that this is not an obligation and that this is not the way to remind people of Allah?

What you said is correct. It is not permissible to invoke evil upon anyone under the pretext that Allah's name was not mentioned, even if the intention is to remind them to remember Allah. We also caution that dhikr (remembrance) using only a single name [of Allah] is not permissible; it is an innovation in Islamic law and grammatically incorrect, as a mere name is not a complete utterance. It has been authentically reported from the Prophet, peace and blessings be upon him, that the best words after the Qur'an are four: "Subhanallah (Glory be to Allah)," "Alhamdulillah (Praise be to Allah)," "La ilaha illa Allah (There is no god but Allah)," and "Allahu Akbar (Allah is the Greatest)."