NEW YORK—A pronunciation slip by President Donald Trump appeared to create a new member of the United Nations on Wednesday, as the U.S. leader lunched with several African heads of state on the sidelines of the annual General Assembly gathering.

An overlooked vowel by the U.S. leader resulted in him praising the progress of “Nambia,” a country that some observers were quick to point out didn’t exist in Africa—or anywhere else.

An...