Under the law, "companies are forbidden to use the official names of countries - both Russian and foreign - as well as their derivatives," the newspaper said.
Companies will also be forbidden to use the names of federal and regional bodies, names "which are against the public interest, as well as the principles of humanity and morality."
Names like 'Russia' and 'the Russian Federation' will only be allowed to be used by companies where the state owns over 75% of the shares.
The regulation could even target the national air carrier 'Aeroflot - Russian Airlines' where the state has a controlling stake. However, the company is set to call on the government to keep 'Russian Airlines' as the brand, an Aeroflot spokesman said.
Russia's new law also applies to foreign companies like Deutsche Bank, Nestle's 'Nestle - Russia' and British American Tobacco, Yevgeniy Arievich, a partner in the Moscow office of the Baker & McKenzie law firm, said.
However, Deutsche Bank vice-president, Olga Podoynitsina, said the German corporation would not be affected by the new law as the word 'Deutsche' is not a derivative of the Federal Republic of Germany, the country's official name.