Traditionally, private law firms choose their names according to the names of the managing lawyers. If a firm has more than two managing lawyers, its name would normally include only these lawyers' last names, such as "Baker & McKenzie", or "Jones, Day, Reavis, & Pogue". For solo lawyers, the name could be based on the lawyer's last name or full name, such as "The Law Office of Doe", or "The Law Office of Jane Doe".
The main reason behind this naming practice is of course professional pride. The lawyers of the law firm are proud of the high level of professional service they offer, such that they want to identify the practice by their personal names. Professional pride, however, is not the only reason why so many law firms have followed this naming practice. Before 1983, the laws of all states required the name of a law firm to identify the lawyers practicing in the firm. This requirement was based on a set of rules governing lawyers' conducts established by the American Bar Association (ABA).
You may wonder whether this naming rule violated a law firm's right of freedom of speech. Indeed, such type of naming rule was challenged in the Supreme Court in the case of Friedman v. Rogers (1979). The Court, however, upheld the states' constitutional right to regulate the naming practice of a professional company.
In 1983, four years after the Supreme Court's ruling, however, ABA passed a new set of lawyer rules. The new rule generally permitted law firms to choose a name that does not identify any lawyer of the firm, as long as the name is not misleading, deceptive, false, or fraudulent.
It's been over 20 years since ABA established the new naming rule. But, not all of the states have adopted it. Based on my preliminary research, 39 states and the District of Columbia have adopted the rule. (AL, AK, AR, CA, CT, DE, FL, GA, HI, ID, IL, IA, KS, LA, MA, MD, ME, MI, MN, MO, MT, NH, NC, ND, NM, OK, OR, PA, RI, SC, SD, TN, UT, VT, VA, WA, WV, WI, WY.) On the other hand, 11 states still require a law firm name to properly identify the lawyers practicing in the firm. (AZ, CO, IN, KY, MS, NE, NV, NJ, NY, OH, TX.)
This disparity may pose a problem for multi-jurisdiction law firms that use non-traditional names. For example, let's say a law firm is incorporated in Illinois, which has adopted the new naming rule. The law firm chooses the name "MagCarta, LLC". (Just something popping up in my head.) The law firm proves to be a success, and it plans to expand to New York. Because New York has not adopted the new naming rule, however, the law firm must choose a different name in the state. This means potential loss of name recognition. (Currently, the New York Bar Association is considering whether to adopt the new ABA rules. See New York County Lawyer Association Newsletter, December 2005, P. 1.)
Personally, I favor less regulation on the name of a law practice. As long as the name is not misleading, deceptive, false, or fraudulent, it is the level of professional service that will truly identify a law firm.