Same transliteration because they are read the same. Romaji (Latin characters used to phonetically transcribe Japanese words -- "Satoshi" in this case) are based on the phonetics of the word. If two words have the same pronunciation but different kanji, they'll be transcribed the same way in romaji.

This is equally true for hiragana and katakana (the other two Japanese writing systems, which are phonetic) and all the names would be written as さとし in hiragana.