Is it permissible to change the name from "Abd al-Qadim" to "Abd al-Qadir"? And which of the two is more correct Islamically: "Abd al-Qadir" or "Qadir"?

There is no legal impediment to changing a name if the change is for the better, as long as it does not lead to harm. It is permissible to be named "Qadeer" (without the definite article "al-"), but if the intention is "Abd Qadeer," it is more correct to be named "Abd al-Qadeer" (with the definite article "al-"), because the names most beloved to Allah are those that express servitude to Him.