Definition:

Believing that a person has the right to a person has the right to adopt, assume, or use any name they want as long as it isn't defrauding or hurting anyone else, many states allow a person, including a child, to change his or her name by using the common law rule.

Under the common law rule, all you have to do is use your new name "consistently, openly and non- fraudulently, without interfering with other people’s rights."
Source: WLCMD.org

Another way to change your name is to have a court proceeding by filing a petition with a local court.

English Common Law View of Name Change:

"Historically, the husband and wife customarily adopted the name of the spouse with the most property and since men typically held more property than women, most women took the husband's name ... This custom never became law, and the English common law view was that a woman's surname was not bound to her marital status and arose only through her use of a name ... Moreover, the right to adopt another name was not limited to males or females ... The concept that the husband and wife are one, the 'one' being the husband, has been abandoned ... Insistence that a married couple use one name, the husband's, is equally outmoded."
Source: SSA.gov
Examples:

"No individual may adopt a name with the intent to defraud or misrepresent him or herself."
Source: SSA.gov