To start, My last name is pronounced "Your-EE-AR-TEE", using the English pronunciation. I guess it makes sense once you understand how it's supposed to sound, but I'm quite used to getting it butchered - no offense taken if you do. I often travel to places where they don't speak English as their first language - if I'm in one of these countries or if I'm speaking French, I will often pronounce it "Or-EE-AR-TAY" (I think this is how it's supposed to be pronounced). My paternal grandfather was Basque and moved to the US, albeit briefly, in the 1970s.
The name is Basque. The Basques are comprised of about 2.25 million people in Northern Spain and Southern France. They are often believed to be the oldest ethnic group in Europe. They are somewhat culturally isolated from both Spain and France and have a certain sense of autonomy from both of those nations. In 1979, three Spanish Basque Provinces of Vizcaya, Guipzcoa, and Alava were united under the Basque Autonomous Government, which has its own governmental parliament. The Spanish province of Navarra is not a member of the Basque Autonomous Government, but is an autonomous region of its own. The French Basque region has no official standing with the French government.
The Basques speak their own language, often referred to by English speakers simply as "Basque". The official name of the language, however, is "Euskara". Euskara is the official language of the provinces under the Basque Autonomous Government. It is, perhaps, the most puzzling modern language spoken today, as linguists have failed to trace its origins, thus it is considered by scholars to be a language isolate. It doesn't look or sound anything like French, Spanish, Portuguese or English. There really aren't any solid clues as to where the language - or the Basques themselves - came from.
In Euskara, my last name, Uriarte, roughly translates to "the house between a group of houses" or a "house between towns" - although I have heard various theories on this interpretation. Go figure.
It is considered a somewhat common name in the Basque country. When traveling in Spain, people have often asked me if I am Basque or if I speak Basque, usually after seeing my name on my credit card or when checking into a hotel. Once in a while, people tell me that there is a famous type of pottery made in Mexico, called Uriarte Talavara (I recently was able to visit their Polanco, Mexico City boutique). There is also an electrical supplies manufacturing company in Spain, called Uriarte Elektro, which happens to be headquartered in the heart of the Basque region. Lastly, theater buffs in New York would often ask me if I was related to Sarah Uriarte, the Broadway actress and singer who starred in many musicals, most notably as "Belle" in Disney's Beauty and the Beast. Nope: No relation that I know of.
You can read much more information about the Basque language and people here: