What is the ruling on being named "Abd Al-Dayim," and is it better than the name "Ali"?

"Al-Daim" (The Everlasting) is not a name or attribute of Allah in the Qur’an or Sunnah. Therefore, it is impermissible to be named "Abdul-Daim" (Servant of the Everlasting), because the names and attributes of Allah are determined by divine revelation (tawqifiyyah). If your common name is "Ali," then make it your official name and abandon the other one.