Was English the predominant language in Ireland during this time? According to Wikipedia, English rule of law was reinforced and expanded in Ireland during the latter part of the 16th century. So, I would assume that's the case? Would, therefore, Irish people being born around this time be named Henry and John instead of Einri and Sean?
What would the Irish and English call German speakers during this time period?
Was there a history of Germans immigrating to Ireland or England during these centuries?
Context: I'm exploring family history, and the 2 oldest ancestors I could find were named Henry and John Germany. I'm trying to figure out why/how they got the surname 'Germany.' A theory I've heard is that they immigrated to Ireland from Germanic lands and were called 'the German' (e.g. Heinrich the German) until it turned into a surname at some point.
There is little in my library that even begins to touch on these questions. While your assumption may be correct, I actually am not sure just from a very brief ancestry.com search. On that site it seems that majority of people with surname "Germany" are from Eastern England in counties that, as far as I can determine, are not heavily Irish. From this information, if your assumption is correct, then I would investigate the surname coming from England instead of Ireland. If your family is Irish then possibly they migrated from England after gaining this unique surname. However, there were some Germans that migrated into Ireland in the early 1700s: from the Lower German Palatinate so maybe your ancestors were part of this pattern.
From what I recall, English did not become the dominant language in Ireland until the mid-nineteenth century. Rural areas and farmers on Anglo-Irish estates spoke Irish-Gaelic even after the Norman "conquest" and implementation of Plantations. While urban residents of the island may have used Anglicized versions of such names, throughout much of Ireland Sean and Einri (to use your examples) would've remained in use.
You may be better off with /r/Genealogy in your search. Good luck!