I just realized my reply before was just to the original email. I will quote it below, but one of the things I ran into was searching for Kiev on the Guardian's website still returns old news stories, and advertisements so it looks like there has been no news for Kiev for over a year. When sites make the change, they should link for searching the previous usage.
Also it was transliterated from both Ukrainian and Russian to Kiev until new transliteration guidelines were published by the government in the early 1990's, and the Ukrainian government started using it in 1995.
Here is my previous reply:
What you see picking your time zone in an app or operating system is set by that app or operating system downstream of tzdb. For example America/Los_Angeles is replaced by a different city in the time zone on many systems. You also don't see the underscore in many apps. Just like they can omit the underscore or use a different city name, individual apps and operating systems could use Kyiv. When procuring computers your government could request or require in the contract that the vendor follow the governments naming convention. This can lead to the change carrying over to consumer software/hardware from the same vendors.
When a change is made to tzdb, it can potentially break every system downstream of it. It makes more sense for systems downstream to change.
Examples go both ways. Yes, the Guardian has changed it in their style guide. That change was less than a year ago, and their search should link the two spellings. Otherwise it might look like nothing news worthy from the Ukraine if you search their site. The site search brought up several ads for travel to Kiev or Kiev hotels. The most recent usage was just less than a year ago - https://www.theguardian.com/world/2018/may/29/russian-journalist-arkady-babchenko-shot-dead-in-kiev
BBC is using Kiev still in a news story as of today - https://www.bbc.com/sport/football/48206280
NY Times used Kiev on May 1 is another story - https://www.nytimes.com/2019/05/01/us/politics/biden-son-ukraine.html
I didn't go past the paywall to see which one the WSJ used - https://blogs.wsj.com/frontiers/2019/04/28/this-week-on-the-frontiers-9 but was presented with an ad for a travel site advertising Kiev hotel bookings. Unlike the Guardian it wasn't in the search results, but it did appear on the page.
Washington Post - https://www.washingtonpost.com/opinions/2019/05/07/us-ambassador-ukraine-is-recalled-after-becoming-political-target/
In addition to comparing google results, I think those news organizations have a fairly wide readership and make a decent benchmark. The majority appear to still be using Kiev.