That is a very interesting concept, thank you, i was not familiar with it.
Both in Russia and in Brazil, names attached to a person have no alternative spellings. If your name is spelled in a specific way, any other spelling is considered a mistake. So for example my name is spelled Tatyana, and if they write it as Tatjana or Tatiana, it will be considered wrong. And if they spell Tatjana Flade as Tatiana or Tatyana, that also will be considered wrong. Aljona Savchenko will be Aljona, not Aliona or Alena. And so on.
In the US, there are a variety of accepted transliteration alphabets. You can see how they compare
here; speaking personally, as someone of Slavic heritage, my surname has been rendered in a variety of ways, to the point that only two constants and a vowel are constant between the French and more standard Romanization efforts. As for Evgenia/Yevgenia, however, I am not a journalist, but generally you would expect to see a publication (and journalist) stick to one transliteration alphabet, except in the case of a person requesting or otherwise making it clear that they prefer their name be rendered differently. So why NBC uses Yevgenia but not Yelizaveta is something I can’t answer, and looks like a lack of editorial direction, as I would expect a copy-editor to catch that kind of inconsistency. However, it’s also very likely that neither the author nor anyone whose responsible for publication has much familiarity with Russian, so the fact that the transliteration isn’t consistent might not have been noticed. I can’t say much more than that.
The way the names are transliterated is not an error made in disrespect or a spelling error, however — that’s an issue related to Romanization. Now, if you tell me you prefer your name to be Romanized “Tatyana,” even if the transliteration alphabet suggests “Tatiana,”
then there’s a question of rudeness, as your preference should be honored. Yuna had issues with this (Yuna Kim, Kim Yuna, Yu-na Kim, etc.), which
was recapped here; ultimately, the Associated Press (AP) went with Yuna Kim at her request. So in instances in which there’s no stated preference, a publication will default to its rules regarding transliteration of a given language, but if there’s an expressed preference, that’s prioritized. Absent Medvedeva making it clear how she would like her name Romanized, we don’t actually know — the ISU rendering may not be her preference.
It’s a giant “Who knows?” but I can attest that Cyrillic is nowhere near the migraine that are known as the Semitic languages! (I used to speak and read a bit of Russian, as well as both an Arabic dialect and Modern Standard... and some Hebrew and Yiddish. It can be worse. Trust me, it can definitely be worse.)