It's like the English words 'naїve', and the original version of the word 'Hawaї' (before it was changed to 'Hawaii'. Same goes for the capital city of Ukraine: 'Київ' - should accurately be spelled as 'Kyїv' - with the 'ї' indtead of the 'i'- if you use this analogy. (It 'looks' better than 'Kyyiv', and is 'cooler' than 'Kyiv'.) ;)
Actually Ï in naive has totally different meaning from Ї in Київ. In English (like in French) two dots make diaeresis, which means that this letter does not make one sound with previous letter. Ï in naïve makes it "наів" (if you try to type it in Ukrainian). Not "нейв" in English and not "нев" in French. The same is for word "coöperation" which is "коопєрейшн", not "куперєйшн".
So, no, Kyiv should not be spelled as Kyïv in English.
Hawaï in French has ï for exactly the same reason as naïve, to make it "аваі", not "аве".