What's the term that describes our data processes
For advertising purposes, you could use the term "Business data enhancement engineering"? :-) Personally, I would call what you do "[complex] [business] data processing". 


  Thanks. Any suggestion on what terms I should be googling for if I
  want to find new tools for our processes?


Just various combinations of what you already do - etl/data warehousing/complex data processing... without knowing a bit more, I can't really be that helpful. Unless, that is, you give the tools that you're using.

However, tool recommendations are off-topic here (unfortunately in my view, but there you have it). Maybe if you have some more specific question(s) that we could help with? You could also possibly try software recommendations?

Oh, and I would (slightly) revise my comment description of what you do - call it "complex business enhancement data processing" or "business complementation data analysis and processing" (cringe...) :-).

Just a note - if you're dealing with more technical people, steer clear of the "marketing speak" - otherwise, go for it! :-)


  We use hand coded SQL, Python and DSL scripts currently, so no
  specific tools so far. We are evaluating whether to improve our DSL
  tool chain, or to introduce some commercial UI tools.


I would also examine the Open Source arena if I were you - there are some pretty awesome tools/products out there! Best of luck!