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The standard brass instrument valve system is the first valve being 2 half steps, the second being 1 half steps, and the third being 3 half steps. Is there a name for this set up? And what are some other set ups or variations that have existed throughout history?

I don't know the name for the current system, but I have seen other systems out there...

French tuning: 1st valve whole, 2nd valve half, 3rd valve 2 whole steps.
I have seen some 19th century horns tuned as such: 1st valve half, 2nd valve whole, 3rd valve 2 whole steps.
There was also a non-zero chance of: 1st valve half, 2nd valve whole, 3rd valve 3 half steps.

Adolphe Sax tuning: 6 valves, each descending a half step further than the last. 1st valve half step, 2nd valve whole step, 3rd valve 3 whole step, etc. *NOTE* these six-valve systems were often dependent on each other, but I have seen examples of independent valves as well.