President Reagan continued to shuffle his Cabinet yesterday in preparation for his second term, announcing that he intends to nominate Energy Secretary Donald P. Hodel as secretary of the interior, and White House personnel director John S. Herrington to take over the Energy Department.

Reagan also announced that he will nominate William J. Bennett, now chairman of the National Endowment for the Humanities, as secretary of education, succeeding T.H. Bell.

It also was announced that Richard G. Darman, one of the most influential White House officials during Reagan's first term, is to become deputy treasury secretary under James A. Baker III, the White House chief of staff, with whom Darman has been closely associated. Reagan earlier this week nominated Baker to become treasury secretary, succeeding Donald T. Regan, who will take over Baker's White House post.

Meanwhile, administration officials said yesterday that several possible government reorganization schemes have run into difficulty.

At a Cabinet meeting yesterday, Secretary of State George P. Shultz raised "quite vigorous" objections to a plan that would consolidate trade functions in a new Department of International Trade and Industry, the officials said.

Reagan earlier promised Commerce Secretary Malcolm Baldrige, chief architect of the idea, that he would support it, but officials quoted Shultz as telling Reagan, "I wish you hadn't done this."

White House spokesman Larry Speakes said the president has taken the trade proposal "under advisement." The plan would consolidate trade functions currently at the Commerce Department and the Office of the Special Trade Representative. Several agencies now at Commerce and not related to trade issues, such as the Census Bureau, would be spun off.

Despite the objections, officials said they still expect Reagan to approve the new trade department, although key details remain to be worked out, particularly the fate of the agencies not associated with trade. What happens to these agencies, which also include the National Oceanic and Atmospheric Administration, is one of the key factors in whether Congress goes along with the plan.

Officials also said it was unlikely that Reagan would seek to merge the Energy and Interior departments any time soon. Reagan promised in his 1980 campaign to eliminate the Energy Department but the idea met with stiff congressional opposition.

Recently, a proposal to merge the two departments was discussed by senior officials, including White House counselor Edwin Meese III, whom Reagan has nominated as attorney general, and outgoing Interior Secretary William P. Clark, who is returning to California.

The nomination of Hodel to succeed Clark was reported earlier and had been expected since Clark told Reagan over the New Year's holiday that he wanted to go back to is ranch.

Speakes said yesterday that Reagan had instructed Hodel and Herrington, once they are confirmed by the Senate, to "commence a study" about the "advisability" of merging their departments and give the president some options.

But other officials said this was probably a death knell for the merger. "The decision to appoint another secretary of energy was the decision to abandon that scheme," one informed official said. He added that senior officials were concerned that a merger proposal would run into serious congressional opposition and put the Herrington nomination in jeopardy.

Speakes told reporters that the study should produce options "designed to recognize the interrelationship of energy, natural resources and defense policies. The president is committed to maximizing effective management and efficiency in the natural-resource area."

Speakes said that Reagan remains committed to the "goal" of eliminating the Energy Department but that the study "does not constitute a decision" to scrap it.

Reagan also promised in 1980 to eliminate the Education Department, but plans to downgrade it to the level of a foundation were resisted by Congress in his first term. With Bennett's nomination yesterday, Reagan asked for another study to "determine the proper organizational structure and the role of the federal government in education." Speakes noted that the foundation idea went nowhere in Congress.

Officials said Reagan's request for another study indicates that it will be some time before the president seeks to abolish the department.

"Congressional approval is required to do anything," Speakes said. "We will work hand in glove with Congress."

Speakes announced the new Cabinet choices yesterday; in the past, Reagan almost always has made the announcements himself, as he did earlier this week in announcing that Baker and Regan would be swapping jobs.

Darman will succeed R.T. McNamar and become the second-ranking official at the Treasury Department. At the time of the announcement, Speakes said he did not know of McNamar's plans; McNamar later issued a statement saying he told Regan last fall that he intended to return to California this year.

Officials said there was no discussion at yesterday's Cabinet meeting of still another government reorganization idea: combining the two water-project agencies, the U.S. Bureau of Reclamation and the Army Corps of Engineers. The president has asked officials to come up with a plan for consolidating them.

There was mixed reaction to yesterday's announcements. Environmental activists generally criticized the Hodel nomination, but some industry representatives praised his selection. Charles DiBona, president of the American Petroleum Institute, described Hodel as "an able and unusually well-qualified nominee for this important Cabinet post."

But the nomination received a cool response from others, including Rep. Morris K. Udall (D-Ariz.), chairman of the House Interior Committee, who said he was "disappointed" at the choice. "Hodel's move will result in a period of unanticipated and divisive reorganization for both departments," Udall said, referring to Energy and Interior.