I have a Chinese name because I’m ethnically Chinese. My country’s everyday language is English, but because of multilingual policies, my Chinese name is in official records, and I’d frankly like to use my name for more than just Chinese homework in school, so I’d like to use it if I were staying in Japan. However, the kanji combination in my name really rare even in Chinese (my parents didn’t follow traditional naming conventions), so I’m not sure how that would go – other Chinese speakers always get the first character wrong, even my tuition teachers. Also, if I use on’yomi in Japanese, my name sounds like the name of a temple in Yokohama (徳恩寺 – incidentally, the first character is what people guess my name starts with in Chinese). Not sure if that’s a good thing or if it would just make my name seem strange.
More importantly though, I have a friend studying at a Japanese university who is like me – we both have an English name and an official Chinese name – and he told me he sticks to katakana. I don’t fully understand why, but he said that using kanji, for example on the door plaque for his apartment, would just complicate things. Maybe it’s because most of our documents and records are in English. I’ll have to talk to him about this in more detail if I really do end up heading to Japan for a few years, but my impression is that you should stick to katakana for anything official unless you have an official name in kanji that you use all the time.
It’s true that many Japanese people struggle with English, but they should know enough to attempt to pronounce your name as it’s spelt. It’s probably more helpful to provide your preferred pronunciation of your name in katakana if there’s a place for such a thing in the paperwork. Changing your official name (within Japan, at least) will probably have to come later. Maybe you can start by using 狼 as a nickname, and then choose a Japanese name you like containing that kanji if/when you are granted citizenship.
By the way, another reason to stick with katakana (at least for now) is that you’ll need to make a hanko (personal seal/stamp) on arrival for stuff like opening bank accounts, and you’ll probably want something that matches your current identity documents and past records. It’ll be a lot easier to get them to accept a hanko that sounds like your name than a hanko containing an unofficial kanji, at least until you have official Japanese documents containing that kanji.
Oops, that was a lot longer than expected. I thought I had managed a short post for once. Anyway, all the best, and I hope you progress quickly in Japanese, because that will definitely make work (and potential citizenship applications) much easier. 
