On this website (in Chinese):
鲁迅”这个笔名,历来有两种解释:一种说法是指“鲁”字乃鲁迅先生母亲的姓,他的小说中常提到的“鲁镇”,就是他母亲的老家;“迅”是他的小名,所以在他的小说里也出现过“迅哥儿”一词。另一种解释是先生挚友许寿裳所说,他亲自问过鲁迅先生,先生笑道:“取愚鲁而迅行的意思。”此乃先生自谦之辞。这两种说法,都是从字面上解释,也切合鲁迅的生平,都说得通。可最近又有人发现了第三种解释。认为“迅”字,古义为狼。出处见《尔雅·释兽》:“狼子绝有力者曰迅。”照这样注解引申出来,“鲁迅”是指狼的一个勇敢有力的儿子。持此一说的是历史学家侯外庐。他说,鲁迅是封建社会的叛逆者,他的小说代表作《狂人日记》就是抨击封建社会“吃人”制度的,他取用这两个字为名,正是鲜明表示他甘以“狼子”自居,与封建社会制度彻底决裂之心声。据说侯外庐的这种解释,曾向鲁迅夫人许广平提起过,许广平连连称谢,表示首肯。
Source: 鲁迅为什么叫“鲁迅”?这个笔名有何寓意? on Baidu Zhidao.
First Explanation: is the author's mother's family name and old home; 迅 is the author's "little name". Sorry, but the original text uses 小名. This is not translatable into English. This name is given to little children, and it may stick as a term used by family and close friends. Sometimes, this "little name" is replaced by the "big name" (大名)or personal name (姓名); sometimes, this "little name" remains as that individual's name for eternity instead of calling that individual by his/her actual personal name 姓名. 大名 and 姓名 are the same thing. It is easy to explain in Chinese: "大名就是大人名字,小名就是小孩名字。" In English, that would be: "Big name" is the name of big people (adults), "little name" is the name of little children.
Second Explanation: 鲁迅 is a joke made by the author: "取愚鲁而迅行的意思". Translation: "pick something that means unclever and fast-moving." This "unclever" word means unclever, dim-witted, or slow mind. The "fast-moving" word means fast-moving. The contradictory meanings between 鲁 and 迅 make up the joke.
Third Explanation: In ancient times, 迅 means 狼 (translation: "wolf"). Wolves are brave and strong. By taking that character as one's given name, it means that he is the son of a wolf, characterizing himself.