Is it permissible to treat with the Beautiful Names of Allah individually, meaning to use one of the Beautiful Names of Allah on a specific organ and not others?

If "Ya Hayyu, Ya Qayyumu" is said in the context of supplication for healing, there is no harm in it, though it is preferable to choose names appropriate for the supplication. However, uttering "Ya Hayyu, Ya Qayyumu" as an absolute, standalone remembrance (dhikr) is not permissible, because remembrance by a single Name is an innovation (bid'ah) that has no basis in Islamic law. The best remembrance after the Qur'an is: "Subhanallah (Glory be to Allah), walhamdulillah (and praise be to Allah), wa la ilaha illallah (and there is no god but Allah), wallahu akbar (and Allah is the Greatest)."