Does the nickname "Majoudi" for the name "Abd al-Majid" constitute mockery of the Beautiful Names of Allah?

There is no objection to calling a son Abdul Majeed by "Majoudi." It was common among early generations to shorten names in this manner, such as "Duhaim" for Abdul Rahman. The derivation or diminutive in this case applies to the person being called, not to the name of Allah the Almighty. Scholars have permitted this unless the person dislikes it or it is intended as a name of Allah, because the diminutive here is for identification or endearment, not a diminutivization of Allah's name. As for diminutivizing the names of Allah, such as "Al-Uzaiz," it is forbidden by consensus.