I am a member of the State Bar of California, the Bar of the U.S. District Court for the Central District of California (San Luis Obispo, Santa Barbara, Ventura, Los Angeles, Orange, San Bernardino, Riverside Counties), and the California and National Associations of Realtors. Please permit me to assist.
There is no specific law that prohibits a business from using the term, "realty" in their name. However, Cal. Bus. & Prof. Code Section 10130(a) provides: "It is unlawful for any person to engage in the business of, act in the capacity of, advertise as, or assume to act as a real estate broker or a real estate salesperson within this state without first obtaining a real estate license...." [emphasis added]
Similarly, Cal. Civil Code Section 1770 prohibits various types of false advertising. Here again, however, the use of the term, "realty" by itself, doesn't necessarily rise to the level of false advertising. But, what you actually do in your business, combined with the use of the "realty" term, could be construed as falsely advertising that you are a real estate professional.
It could be argued by the government that by using the term, "realty" in your business name, that you are advertising as and assuming to act as a real estate broker or salesperson. Whether or not this is a valid legal argument would be up to a court. I think it's a risky bet for you, but I cannot say that it's absolutely illegal.
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