Does cumin contain curcumin? If not, where does the name come from?
From the opening of the Wikipedia article on curcumin you presumably saw:


  Curcumin is a bright yellow chemical produced by some plants. It is the principal curcuminoid of turmeric (Curcuma longa), a member of the ginger family (Zingiberaceae).


(emphasis mine)

As for the Curcuma genus:


  The name comes from the Sanskrit kuṅkuma, referring to turmeric.


So, nothing to do with cumin - just a bit of a coincidence from turning "curcuma" into "curcumin".