Supposedly naming land after field (Pole) is common in Europe. Similar etymology happened to names Compania and Champagnia, I've heard.
Linguistically, I suspect, that name "Pole" came from word "polesie". Polesie is descriptionary word to explain where forest ends. Po - means after, lesie - means forest in locative case.
This area in Europe was covered with dense forest, so it was very useful to have a word describing a place at the end of forest for these people. There are still existing locations named just "Polesie". Also little meadow in the middle of forest is called "polana", and it doesn't mean agrarian land. Just place with no woods, well at least in today's meaning.
I assumed that, in some cases the word "polesie", broke to "pole-sie", and got shortened to just "pole", with meaning empty ground, place with no trees, and agrarian field.
One of the points I was trying to make at the beginning of the thread was that name Polska (in polish) is only attested around 15 century and not necessarily used to describe the full extent of first known "Poland", the land of Mieszko. For first 4 centuries we only know this name in latin, Polonia, Polania, Polenia, even Bulonia, never as Polska. And in this form only describing land of Polans, the tribe of Polanie, and never the whole dominion of Mieszko or Chrobry. I think we have to wait till 13 century to start to see Polonia used for the whole country, and this without Silesia and West Pomerania, which were separated since.