The correct way to write non-Japanese names in Japanese script is to use the katakana alphabet to transliterate all of the sounds in the name to their Japanese equivalents. This is usually straightforward as long as the writer takes Japanese pronunciation rules into consideration. Online tools, such as the Japanese Name Converter and JapaneseTranslator.co.uk, are available to assist in the translation.
Some people try to convert their names to the nearest kanji forms, but this often gives bizarre translations in Japanese because kanji represent ideas rather than sounds. Using katakana creates a proper Japanese form without this difficulty. A few Western names translate into kanji successfully, but these tend to be short names that people sometimes use in Japan already, such as Leo, Tom or Luna.
While individuals can use a katakana chart to translate each phoneme in the name separately by hand, several apps and websites offer instantaneous translations. One of the most straightforward is the Japanese Name Converter by Nolan Lawson, available on PCs and as an Android app. This simply presents a box for users to input an English name, and it immediately produces a katakana version along with the pronunciation of that form. JapaneseTranslator.co.uk offers a dictionary of names with appropriate katakana translations. These are likely to be the most accurate versions available, as Japanese scholars translate them individually, but by its nature, a dictionary cannot contain all possible names.