Which one? Kiev or Kyiv? We don't write Roma for Rome, but we do now write Mumbai rather than Bombay. And really, there's not a lot of difference between the pronunciation of Kiev and Kyiv, at least when I read them.
Transliterations can do some damage to the 'authentic' spellings, particularly when there's a letter in the original that doesn't exist in the other language. "Kiev" is transliterated from Russian, the official language of late USSR. It is also the language many residents speak natively or at least very well. "Kyiv" is transliterated from Ukrainian, which is the official language of Ukraine. It is also the language of historic Ukraine of which Kyiv is the capital.
How did the confusion arise? Well, Kiev is the recognized transliteration of the name of the city in Russian, and also the old Ukrainian name which has been used for centuries (by the likes of national hero, Taras Shevchenko, no less) right back to the times of Kievan Rus. Kyiv meanwhile is the transliteration of the modern Ukrainian name of the city and the official name as far as all legal and political issues are concerned. Following the establishment of an independent Ukraine in 1991, there was a move by many Ukrainians to favour Kyiv as it symbolized a departure from all things Russian, and indeed Kyiv is now used by the UN and many other official bodies as the correct name.
Kiev, on the other hand, is a direct transliteration of the Russian spelling of the city’s name. This provides the main fuel for the argument that this spelling in English represents a relic of Russian domination, in which Ukraine was seen through the prism of Moscow. (It is argued by some that Kiev, in fact, reflects the original, Old East Slavic spelling of the city’s name. This language, an ancestor of Ukrainian, Belarusian and Russian, was used from the 10th to the 14th centuries in Kievan Rus and its successor states.)
To our mind, both the strongest and the most problematic argument for change lies in the claim that Ukraine itself has asserted that Kyiv is its preferred spelling and has urged the popularisation of that spelling. However, English-speakers are by and large still more familiar with Kiev. This is due, in part, to almost every major news organization sticking with the conventional spelling.