What is the ruling on naming a newborn "Aabid Al-Rushdan" or "Ubayd Al-Rushdan"? And which of the two is permissible?

It is not permissible to name a newborn "Abed al-Rashdan" or "Ubaid al-Rashdan," because "al-Rashdan" is not among the Beautiful Names of Allah. Naming someone with "Abed" (worshipper of) names that are not among the Names of Allah is considered a form of disbelief (ilhad), as the Names of Allah are divinely ordained (tawqifiyyah).