Major personnel changes at the Securities and Exchange Commission are leading to a period of upheaval at a time when the agency faces major regulatory decisions.

Last week President Reagan nominated Charles C. Cox, the SEC's chief economist, to replace John R. Evans, whose second term expired June 5. Evans, a moderate Republican, has often clashed on policy issues with SEC Chairman John S.R. Shad. Shad asked the White House to name Cox, despite the objections of the other commissioners, who said Cox wasn't qualified for the job. If he is confirmed, Cox is expected to follow the chairman's lead in taking pro-business positions.

Cox's confirmation hearing will probably be delayed until September, because of the Senate Banking Committee's busy schedule. At that time, Democratic members plan to grill him over his lack of securities experience, but, Hill sources predict, will not vote against him in the end. Evans retains the support of one Republican senator from his native Utah, Orrin G. Hatch, but the other senator from Utah, committee Chairman Jake Garn, switched his support to Cox at the White House's urging.

Some people at the SEC and on the Hill see an effort to strike a deal in which Cox's nomination would be approved in exchange for filling the next vacancy on the commission with Charles L. (Lindy) Marinaccio, the Banking Committee's minority counsel. Several weeks ago, the committee's bipartisan leadership wrote the White House recommending that Marinaccio be nominated.

The letter did not mention whether he should take the seat of Commissioner Barbara Thomas, who recently announced that she would resign this fall, or that of Bevis Longstreth, also a Democrat, who plans to step down when his term expires in June, 1984. But another bipartisan letter sent to the White House yesterday by the committee's securities subcommittee did specify Thomas's seat. (By law, two of the five SEC commissioners must be Democrats.)

However, the administration's concern over its standing with women voters may prompt Reagan to nominate a woman to what is sometimes referred to as the "woman's seat," since it was held by Roberta Karmel before Thomas. Among the names being mentioned for the job are Judith G. Shepard, vice president and associate general counsel of Goldman, Sachs in New York; Linda A. Wertheimer, a securities lawyer with Jackson, Walker, Winstead, Cantwell & Miller in Dallas, and Maryellen B. Cattani, vice president and general counsel of Transamerica Corp. in San Francisco.

In any case, Reagan will have a chance to fill all five commission seats with persons sharing his philosophy of deregulation.

Starting this fall, the SEC will be asked to weigh recommendations of its tender-offer committee that would curb some of the abuses that can take place in corporate takeovers and would generally encourage a more open takeover system.

The commission will also decide whether to approve shelf registration of securities, letting a corporation issue stock without having to refile financial information. The move would simplify the process and save money for corporations, but nevertheless could limit the information provided prospective buyers.

The commission will also have to decide whether banks and brokers who hold shares for customers should reveal their identities to the issuing companies and how to restrain frivolous proxy resolutions.

The commissioners are known to be divided on all of these issues.