My Google-fu is letting me down today.
PU mean in ATmega88PA and ATmega8-16PU?
P for PDIP what is
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I think the confusion here is that ATmega88PA is an actual chip. As you can see from the way it's written, "PA" is not a tag-on package code after a dash but a part of the model number. And yes, the information for the package types and codes is in the datasheet under "ordering information".
This link might help, but it's a little outdated and doesn't seem to mention A and U.