From wiki:
"Reed" is commonly believed to be a nickname-derived surname referring to a person's complexion or hair being ruddy or red.

Etymology and history
Although the name is derived from a common occupation, many later Smiths had no connection to that occupation, but adopted or were given the surname precisely because of its commonness. For example:It is common for people in English-speaking countries to adopt the surname Smith in order to maintain a secret identity, when they wish to avoid being found. Smith is an extremely common name among English Gypsies; see also John Smith