CLEVELAND (AP) _ For marketing purposes in Ohio, it will still be Sohio, but as a corporation, the Standard Oil Co. (Ohio) is taking a step back into its early history to rename itself Standard Oil Co.

The Cleveland-based oil giant announced Monday that as of today, it is dropping the ''Ohio'' from its corporate name, except for marketing gasoline and other products at its familiar Sohio stations in Ohio.

The new name of Standard Oil Co. is an old one in the history of American industry, dating back to 1870 when John D. Rockefeller organized the company in Cleveland to refine oil from Pennsylvania.

Standard Oil Co. grew into the largest corporation in the world before it was broken up in 1911 by the U.S. Supreme Court.

In announcing the change in newspaper ads today, the company pointed to its past history and proclaimed, ''The Standard Oil Company is still the Standard Oil Company.''

A company spokesman acknowledged that top management had worried about a psychological link in the public's mind with oppressive, all-powerful corporate groups in returning to the old name.

''With the founder being John D. Rockefeller, it was a little hard to ignore there were times when he wasn't very popular,'' said Nigel D. Muir, the company's director of public affairs.

Muir said the idea of improving corporate identity arose after Sohio completed the purchase a year ago of about 5,600 Gulf gasoline stations and a refinery after Chevron purchased Gulf.

''We weren't exactly sure how well the company was known among various groups that were important to us,'' he said, including the government and financial communities.

Other name changes in the industry also helped Sohio make its decision about its own identity.

Last spring, Standard Oil Co. (Indiana) chose to change its name to Amoco, which had been the name of its gasoline for many years.

That left Ohio's Standard Oil the only one of the companies created by the breakup that still had Standard Oil in its name. Standard Oil (New Jersey) had become Exxon. Standard Oil of New York had become Mobil, and Standard Oil Co. of California had become Chevron.

The company will continue to use other brand names outside of Ohio, including Gulf in its stations in the Southeast, Boron and BP.