Currently Yandex TTS component has only six hardcoded voices. I found that actually now Yandex has many more voices available, please check their demo page (only available in russian language):
If you inspect the input field which says “Oksana” you will see the full list of supported voices.
It’s a pity that you cannot simply put for example “kostya” in HA config and have that voice right now.
But I can confirm that if you modify the yandextts.py file and add it to the hardcoded list, it will be fine and you get the desired voice.
It would be great if you either add all those new voices to the component, or better yet, remove the hardcoded list at all so that anything could be put as a parameter, if possible.