What is the ruling on naming a newborn "Bashar al-Din" or "Bashar Allah"? And does this name carry a beautiful meaning and conform to Islamic law?

It is permissible to be named "Bashar al-Din" if the intention is the one who supports or serves the religion, and it is permissible to be named "Bashar Allah" if the intention is the one owned by Allah or created by Him, due to the sound meaning they carry. Nevertheless, it is advisable to choose a name with a clear meaning.