I Bet You are Referring to Ukraine Incorrectly.
When talking about my country of service (pictured above), think to yourself what you would naturally call it. Chances are the first thing that came to mind was "The Ukraine" instead of simply Ukraine sans (big T) "The".
First of all, just in case some of your attentions span only last this far, let me say that calling Ukraine, The Ukraine, is offensive to Ukrainians and the incorrect terminology to use.
I was guilty of this myself before I came to Ukraine, as was most of my family. Even Former President Obama referred to Ukraine as "The Ukraine" during a press conference. It happens, and a lot of people are guilty of it. Not out of malice but out of ignorance. "The Ukraine" is what we called Ukraine when it was a part of the USSR. Once you phrase something one way for so many years it just sounds "right". Especially when it concerns something you don’t say often.
I did some research into why exactly that phrasing came about and why exactly it is incorrect. I thought I would share as I actually learned there are other countries I am calling the wrong name as well!
According to Oksana Kysyma from the Ukrainian Embassy in London, " The Ukraine is both grammatically and politically incorrect," 
Lets first look at why we are in the habit of calling it "The Ukraine" in the first place.
Where did it come from?
Referring to Ukraine as "The Ukraine" stems from a time prior to Ukraine's Independence in 1991. Prior to independence Ukraine was known as The Ukrainian Soviet Socialist Republic and it's short name was "The Ukraine".
But what about in Ukrainian? Ukraine as a language does not have articles like we do in English. You would say “The book” and “a book” exactly the same way. Книга. A theory as to how the "The" came to be is that whomever brought the translation over to English knew that Ukraine translated to borderland and that without the "The" borderland sounds weird.
Why it is wrong?
First and foremost, “Ukraine” is the way the they are identified on both their Constitution, and their Declaration of Independence. The name is also recognized without disputed by the UN. Unlike the Burma vs Myanmar debate.
Second, the removal of the "The" is hugely symbolic for Ukrainian people. It is a linguistic independence, in the sense that many Ukrainians believe that by keeping the "The" it unfairly links them as still being a part of Russia and not being a free and independent country.
According to William Taylor, Ambassador to Ukraine 2006-2009 ““The Ukraine " is the way the Russians referred to a part of the country during soviet times... it is incorrect to refer to [Ukraine as] "The Ukraine"”. Taylor goes on to say that the diaspora (Ukrainians now living abroad) "fume" whenever they hear their country referred to in that manner. 
The "fume[ing]" is something I can most certainly attest to. Any time the subject is broached, my Ukrainian friend are very clear on their stance. They want their country to be respected.
Fun fact, a lot of countries have recognized short names. For example, the UK, and the US, when their official name is the United Kingdom or the United States of America. (check the lower cased ts). I did learn that only two countries should be referred to with a proceeding article "The". Those countries are: The Bahamas (the Common Wealth of The Bahamas) and The Gambia (the Republic of The Gambia). Notice the capitalization and lack of capitalization in this paragraph.
That means that calling it "The Philippians" or "The Netherlands" is technically also wrong. However, you might say "Katie it sounds so natural! Why should we believe you" Good question, and good for you for fact checking everything you read! I got this information about official names from "The CIA World Fact Book" ; the Times Comprehensive Atlas of the World; and the US Department of State. So feel free to check those sources out!
Back to Ukraine
According to Mike Ashworth, "Definite articles are attached to areas where they have a mix between geographical names and physical entities.”  The example he states is that you wouldn't say you are going to Maldives but would say you are going to the Maldives because it is the geographical area. The name of the country is the (little t) Republic of Maldives.
Ukraine is not a part of a larger geographical area, and they are not a borderland to Russia, or a wayward former part of the USSR. Ukraine is an independent country, all on its own.
More Fun Facts About Place Names and Articles.
Question. Why do places like the United Kingdom or the United States carry a (little t) the? Well, it is because they are compound nouns . Nouns compounded with adjectives. (Feel free to click the link above if you don't remember much about middle school grammar) (please be assured I didn't).
According to etymologists and linguists, articles for place names appeared in the English language pretty late. In Old English there were no definite articles. I can also tell you that should time travel be possible, (sans a TARDIS) , I would not be able to understand much of Old English anyway. Case and point. <-- (and that isn't even Old English but Middle English.)
Wrapping it up
A lot of this comes down to the fact that Ukraine is a relatively new country and this change is relatively new. Also, if we are being honest, Ukraine isn't talked about that much in the mass media in the states. They do not get a lot of exposure when compared to other countries.
When people refer to Ukraine as "The Ukraine" I know that it is not out of malice, that they are not trying to make Ukrainian people feel bad, they simply haven't been told we don't say that anymore. But that is part of the point of the Peace Corps #3rdGoal , to educate my fellow Americans about this amazing country that I am beyond blessed to serve in.
To see if you are calling the capital the proper name click here.