Is it permissible to be named "Azizur Rahman"? And if not, is it obligatory to change it?

Naming someone "Aziz al-Rahman" is not appropriate because Muslims are not accustomed to it, and because its meaning might imply commendation and illusion. Names that contain commendation are forbidden. Ibn Taymiyyah mentioned that the Salaf did not use names in this manner. As for naming "Abd al-Aziz" and "Abd al-Rahman," it is permissible because these are names beloved to Allah.