What name is given to conversion between data of different widths?
Truncation was the word that was at the tip of my tongue. It's "limiting the number of digits right of the decimal point". So if we imagine that these 16 bits are in fixed point arithmetic and if all bits are = 1 then we got something close to 0.9999, then you could truncate the bits from 16 to 8. Aka throwing away 8 bits. Zeros and ones are just digits in base 2.. 

It's a cheaty way but not necessarily wrong. Not really right either. 



The more correct term would in this case be decimation, the act of throwing away every X data of a signal, where X = "second" or "third" or etc. Since it's on an FPGA and you're streaming data it can be visualized as a signal. 



EDIT:

Ah here's another definition of truncation called data truncation, the first one I linked was regarding math. This data truncation sounds like a perfect fit of what you are describing. 

Or if you just want an umbrella name, there's data loss. 

I believe all 4 would be acceptable in this case.