I have been reading today from a link in an answer here about Medieval names. In particular I am seeing that people stuck very much to names from within their own culture. This is more or less true up to my generation in England but I see that my great-nieces and great-nephews have names from all over the world. Was this a matter of stigma in historical eras (particularly the Tudor) or was it just a matter of not knowing other names?
There was actually quite a lot of borrowing of names between cultures in the Middle Ages -- it's just sometimes hard to see this because so many names were in common use across Europe, so it's not like you can easily say "this name comes from THAT culture and was borrowed into THIS culture". There are exceptions to this, e.g., when Norman names arrived in England and quickly spread beyond use the aristocracy, or when Scandinavian names arrived in Normandy. After the English invasion of Ireland you find a lot of English names infiltrating the Gaelic name stock -- not just in Irish records of the invaders, but being given to native Irish children as well.
All that being said, here are a few examples of names that were borrowed from other cultures into English in the 16th C: Gwenllian (from Welsh, http://dmnes.org/name/Gwenllian); Ferdinand (used in a variety of contexts, but likely imported into England via the Spanish, http://dmnes.org/name/Ferdinand); Teague (an Irish import, dmnes.org/name/Teague). (I'm sure I could find more, but it would take a more systematic search than just looking up the names that I already know of.