When the name Kenji is written in katakana, it appears like this: ケンジ (KEN-JI)
We search for kanji that can be read the same way, and using those phonetic characters, we create a name in kanji.
This time we created the following name in Kanji: 賢治
賢 can be read as “KEN,” and means “wisdom.”
治 can be read as “JI,” and means “govern” or “manage.”
When we combine the kanji 賢 + 治 Kenji’s name in kanji (賢治) is then complete.
(To be honest, there are other ways to write "Kenji" in Japanese kanji, so this is not the only correct way! ).
It’s possible that Japanese people won’t recognize the phonetic reading of 賢治 (Kenji’s kanji) right away, but when presented together with furigana (the katakana pronunciation), they will surely understand.