The immediate example I can think of is the commissioning of William Knudsen as a Lieutenant General in January of 1942. Previously he had been the head of General Motors. He was the Director of Production, reporting to the Under Secretary of War. Although he wore Army uniform, he was responsible for all production, including naval, so perhaps this is the crossover into your question. I can't seem to find anyone meeting the description who was comissioned into the navy. Note, this was not an honorary commission. It was an actual commission, with full force of law and rank. Honorary commissions are exactly that, honorary. The Lt Dan guy does not have legal authority to order sailors around, but Knudsen did.

To answer the process question, General officers (which would include admirals) are commissioned by the President with the advice and consent of the senate. Therefore, the President nominated Knudsen for the temporary rank of LtGen, and Knudsen was duly discussed by the Senate Subcommittee on Military Affairs on 24 January 1942.

A reading of the transcript https://babel.hathitrust.org/cgi/pt?id=uiug.30112119649454;view=1up;seq=7 indicates that Knudsen would have been the first civilian so promoted to flag rank, at least in the modern army. It also goes over the question of if he really needed to be an Lt General to perform the functions of the role.

Further reading, look up "Arsenal of Democracy" by Baime.