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-Basir occurs 42 times in the Quran; its page in the 99 Names section gives its meaning and verses.
ʿAbd al-Basir joins ʿabd with al-Basir, from the root b-s-r of sight and insight: the One who sees everything, down to the most hidden, and knows what His servants do. In the Quran it is almost always joined with al-Samiʿ: “He is the All-Hearing, the All-Seeing” (42:11).
And you will surely find them the most greedy of people for life - [even] more than those who associate others with Allāh. One of them wishes that he could be granted life a thousand years, but it would not remove him in the least from the [coming] punishment that he should be granted life. And Allāh is Seeing of what they do.
And establish prayer and give zakāh, and whatever good you put forward for yourselves - you will find it with Allāh. Indeed Allāh, of what you do, is Seeing.