Does cumin contain curcumin? If not, where does the name come from? According to Wikipedia, curcumin was originally isolated from tumeric.  However, I haven't been able to find why it was  named curcumin or whether or not it cumin is currently known to contain it.
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".