How do I create a field whose name is the value of another field? Like backticks or eval() in other languages.

I have a set of data, perhaps XML, perhaps 5.x+ PerfMon, and it's in this format:

aName=Field1 aValue=123
aName=Field1 aValue=234
aName=Field2 aValue=345
aName=Field2 aValue=456

I would love to do a | stats avg(Field1) avg(Field2) but I can't get at the values!

How can I create a field with the name of aName, and the value of aValue? This is very similar to backticks or the eval() function in other languages.