A law that establishes the official use of the name "God" in government mottos, oaths, etc., to mean a generic deity that is of no particular historic significance and that would not provide any right or claim by any religious organization to claim that "God" as used by the government, is a specific god because of the historical religious beliefs of America's founding fathers.
The intent of the language would be to provide inclusiveness to all faiths and to avoid the assertion that God is a particular god in reference to the United States of America.
Defining the government's use of the name "God" in no way shall endorse a particular religion, nor imply that any particular god is the official god of the United States. Use of the term "God" shall not imply a common belief in any deity.