Is a person sinful for writing his apparent name in an email in English, knowing that "ratana" (rattling/gibberish) is defined as Arabs speaking a language other than Arabic, and given that the person does not speak with others in English?

There is no sin in writing emails in English or any other language, nor in speaking them. Al-Bukhari included a chapter titled "Whoever Spoke Persian and Gibberish," and Al-Ayni permitted speaking in languages other than Arabic out of necessity. He pointed out that the Prophet, peace and blessings be upon him, ordered Zayd ibn Thabit to learn the languages of the non-Arabs. It is disliked to speak in a language other than Arabic if some of those present do not understand it.