I got used to hear a little bit of the history of the name Libera.
I don't know if it is without errors, but most parts should be correct.
At first I must mention, that the name libera has not been the name of a family but rather the name of people living within a special area. This Area is Schlesien (formar name in history), today part of Poland.
As long as I know it used to happen, that our ancestors have been moving to that area in the 17. century because it was neary unpopulated after a outbreak of black plague and/or a war lasting 30years at this time. The people moving there wanted to get rid of the feudal system and wanted to live a life without aristocracy.
As long as I heard they tried to build up some sort of democracy, but I don't know if that part is true.
So it might be, that we don't share the same genoms, but rather the same history.
I hope this helped a little bit in order to answer some questions.
But if something is incorrect feel free contact me.