Gen. Bennie L. Davis, commander of the Strategic Air Command since 1981, will retire Aug. 1 after more than 35 years of service, the Pentagon has announced. President Reagan has nominated Gen. Larry D. Welch, the Air Force vice chief of staff, to replace Davis, the Pentagon said.

Reagan announced yesterday that he is nominating career diplomat Edward Joseph Perkins to be ambassador to the Republic of Liberia. Perkins, 56, director of the Office of West African Affairs in the State Department, would succeed William Lacy Swing.

Earlier, Reagan said he would nominate John Arthur Ferch, a Foreign Service officer who has served in Cuba for the past three years, to be U.S. ambassador to Honduras. Ferch would succeed John D. Negroponte.

Reagan also announced the appointment of Russell F. Miller to be deputy inspector general of the Synthetic Fuels Corp., succeeding Robert Gambino. Miller is Synfuels' director of investigations. He previously has served 29 years with the Central Intelligence Agency.

At the Health and Human Services Department, officials took pains to deny reports that Dr. Everett R. Rhoades, the first Indian to head the Indian Health Service, will be dismissed or will resign.

Dr. Robert Graham, head of the Health Resources and Services Administration, said HHS Secetary Margaret M. Heckler "was dismayed to learn the rumors had surfaced" while she was away on business. Graham quoted Heckler as saying Rhoades has served with "honor, energy and innovation" and that "she has no intention to replace him."