Is there a name for "chips out of which one can build a CPU"?
You need to be able to do NOT and one of AND and OR. Using Demorgan's laws, either of these functions can be transformed into the other, and thence into all other logical functions. 

This is known as functional completeness or expressive adequacy.  The components or functions which create such a system are known as Sheffer functions (after Henry Sheffer, who published a proof on the topic) or sole sufficient operators.  

Also of interest is the fact that you can combine a quartet of NAND gates to make a D-type flip flop, and from there a memory cell, which is also required to create Turing completeness.

ProofWiki's article on the topic is good reading.