Correct spelling for the English word "Adrain" is [ɐdɹˈe͡ɪn], [ɐdɹˈeɪn], [ɐ_d_ɹ_ˈeɪ_n] (IPA phonetic alphabet).
The word "Adrian" is of Latin origin and is derived from the Roman family name "Hadrianus", which was derived from "Hadrian" or "Hadriani" in Latin. This name was originally a cognomen, meaning it was a third name given to an individual that often described a personal characteristic or feature. In this case, "Hadrianus" is believed to have derived from the Latin word "hadros", meaning "dark" or "black". The name gained popularity due to the Roman Emperor Publius Aelius Hadrianus, commonly known as Emperor Hadrian, who ruled from 117 to 138 AD. As a result, the name evolved into "Adrian" in English and has been used as a given name ever since.