The Prophet ﷺ said: “The most beloved of your names to Allah are ʿAbd Allah and ʿAbd al-Rahman” (Muslim 2132), and scholars add to them all names formed on a name of Allah. The name al-Quddus occurs 2 times in the Quran; its page in the 99 Names section gives its meaning and verses.
ʿAbd al-Quddus joins ʿabd with al-Quddus, from the root q-d-s of purity and holiness: the One free of every flaw and imperfection. The same root gave al-Quds, the Arabic name of Jerusalem. The name is rarer than other ʿAbd names, but known from North Africa to South Asia.
He is Allāh, other than whom there is no deity, the Sovereign, the Pure, the Perfection, the Grantor of Security, the Overseer, the Exalted in Might, the Compeller, the Superior. Exalted is Allāh above whatever they associate with Him.