For Japanese names, we often match the sounds of the names' letters with the Chinese characters that have their meanings.
ご質問ありがとうございます。
「あてがう」または「当てはめる」は"match"を使えると思います。
"For Japanese names"=「日本人の名前には」
"we often match the sounds of the names' letters"=「名前の文字の音を~に当てはめることが多い」
"with the Chinese characters that have their meanings."=「意味がある漢字と一緒に。」