The White House yesterday announced a number of nominations to State Department and ambassadorial posts, including the envoys to Lebanon, Saudi Arabia and Great Britain.

Reginald Bartholomew, a career Foreign Service officer and the negotiator in talks with Greece on American military bases there, has been chosen to be the new envoy to Lebanon. If confirmed by the Senate, he would replace Robert Sherwood Dillon. Walter Leon Cutler, now ambassador to Tunisia, will move to Saudi Arabia to replace Richard W. Murphy, who is to become assistant secretary of State for Near East and South Asian affairs.

Charles H. Price II, a longtime personal friend of President Reagan and the current ambassador to Belgium, was nominated to be ambassador to Great Britain, replacing John J. Louis Jr. Businessman Geoffrey Swaebe, now U.S. representative to the European office of the United Nations, was nominated to replace Price.

Frank V. Ortiz, now envoy to Peru, was named to the same post in Argentina. He would replace Harry Schlaudeman, who left to serve as chief of staff for the president's commission on Central American policy. Nicholas Salgo has been nominated to succeed Harry E. Bergold Jr. as ambassador to Hungary. A businessman and a native of Hungary, Salgo has been a consultant to the U.S. Information Agency since 1982.

Gerald E. Thomas, now envoy to Guyana, was named to that post in Kenya. He would succeed William Caldwell Harrop. And Joan M. Clark, director general of the Foreign Service, was chosen assistant secretary of State for consular affairs, succeeding Diego C. Asencio. She will be replaced by Alfred L. Atherton, now envoy to Egypt.