[Nyororin]

No, you DO have to choose a Japanese name.
It has to follow the same rules as other Japanese names, barring use of certain characters, etc. This rules out keeping the same name and simply writing it in katakana.

It does not have to carry the same pronunciation or meaning as your original name - but you WILL have to change both your first and last name if you receive citizenship. Most people do choose something either similar in pronunciation to their original name, or a Japanese name with similar meaning.