"小名" 用英语叫做 "nickname"。
Nickname 是由英文 "nick" (昵称) 和 "name" (名字) 组合而成的词。
例如:
"He goes by the nickname 'Big Mike'." (他被人称为"大迈克"。)
"Her nickname is 'Lola', but her real name is Karen." (她的小名是"洛拉"，但她真正的名字是卡伦。)
"He has a lot of nicknames, but his favorite is 'Buddy'." (他有很多小名，但他最喜欢的是"巴迪"。)