Question: Yesterday I was practising katakana by writing my classmates' names down, but some of the names were harder than I expected. I have a classmate named Väinö, but neither the ä or ö sounds exists in Japanese. At first I considered writing his name down as Waino, but that sounds like the word vaino which means persecution in my native tongue. How should I write these vowels?

Has anyone had similar problems? How did you solve them?

Answer: 
unfortunately, Japanese is not well suited for representing the sounds of words or names in other languages. Listening to that name online (assuming it is the Finnish name that I found the pronunciation for) the closest katakana would be 
ヴァーイネ　which in romaji would be written Vaaine or Va-ine. Some people might choose to write the katakana 'ne' (ネ) half-size, which in Japanese represents that the sound should be minimized in some way. There are standard and well understood versions of this like ファ、フェ、so you might get Japanese to a closer approximation of your friend's name with 'Vaainue' where the katakana 'nue' is written ヌェ. Or go the other way and write it 'Vaaineu' with a minimized 'u' sound.

Japanese people know that katakana cannot accurately represent the sound of other languages well, so most of them will take care to listen to how your friend pronounces his name, and try to mimic him. But for people seeing his name in print and never hearing the proper pronunciation, expect to have to help them get it right upon meeting them.
When transcribing your name to Japanese, in principle you can choose a transcription as you please.

For transcribing V, ヴァ・ヴィ・ヴ・ヴェ・ヴォ *va vi vu ve vo* is standard. (See this question, though: [Do Japanese actually pronounce the "v" sound?](https://japanese.stackexchange.com/q/24498/1628))

As Japanese has only five vowels /aiueo/, vowels which are different in your native language will have to be mapped to the same vowel in Japanese.

A common strategy is to ignore the diacritics and substitute Ä ­­→ A → /a/, Ö → O → /o/, etc. (not only in Japanese, but also in English!).

This also seems to be common for well-known people named Väinö:

* [Väinö Raitio → **ヴァイノ**・ライティオ](https://ja.wikipedia.org/wiki/%E3%83%B4%E3%82%A1%E3%82%A4%E3%83%8E%E3%83%BB%E3%83%A9%E3%82%A4%E3%83%86%E3%82%A3%E3%82%AA)
* [Väinö Siikaniemi → **ヴァイノ**・シーカニエミ](https://ja.wikipedia.org/wiki/%E3%83%B4%E3%82%A1%E3%82%A4%E3%83%8E%E3%83%BB%E3%82%B7%E3%83%BC%E3%82%AB%E3%83%8B%E3%82%A8%E3%83%9F)
* [Väinö Linna → **ヴァイノ**・リンナ](https://ja.wikipedia.org/wiki/%E3%83%B4%E3%82%A1%E3%82%A4%E3%83%8E%E3%83%BB%E3%83%AA%E3%83%B3%E3%83%8A)
* [Väinö Hannikainen → **ヴァイノ**・ハンニカイネン](https://ja.wikipedia.org/wiki/%E3%83%B4%E3%82%A1%E3%82%A4%E3%83%8E%E3%83%BB%E3%83%8F%E3%83%B3%E3%83%8B%E3%82%AB%E3%82%A4%E3%83%8D%E3%83%B3)

If that doesn't work for you for some reason or other, you can try to modify it to ヴァイネ *Vaine*. (Note that Ö [[ø]] → /e/ is also standard for transcription from German, as for example in **Kö**ln → **ケ**ルン, **Gö**ttingen → **ゲ**ッティンゲン, Goethe [[ˈɡøːtə]] → **ゲ**ーテ, etc.)