When I first came to Japan in 2007, the secretary of my lab in Tokyo registered me in all kinds of places. For this she not only had to give my name but sometimes also a Japanese transcription. For this she called me Saimon Kasupa Shunaida, サイモン カスパー シュナイダー.
The secretary of my new lab, though, did her homework and registered me at the university with the proper spelling of my last name, as Saimon Kasupa Shunida, サイモン カスパー シュニーダー.
This only became a problem when I told them that I still had a bank account in Japan under my old name. As it turns out, the university can only pay my salary to an account registered under my own name and my old bank account does not fulfil that criterion.
No need to worry, though. I just went to the bank and asked for a name change. For this, I think, they gave me the form sheet which they normally use when someone changes their name due to marriage.