WASHINGTON — President Trump shared a photograph on Monday of the “wonderful” dog who participated in the raid against Abu Bakr al-Baghdadi, the Islamic State leader, but said the dog’s name remained classified.

The president tweeted out the photograph after Gen. Mark A. Milley, chairman of the Joint Chiefs of Staff, had given an update on the dog, whose role in the raid was first disclosed by Mr. Trump on Sunday.

“We will not release the name of the dog right now,” General Milley told reporters at a news conference giving new details on the raid. “But the dog is still in theater, returned to duty. So we will not release just yet photos or names of dogs or anything else.”

But by late afternoon, Mr. Trump had apparently received special dispensation to post an image of the dog, whose name Newsweek reported is Conan. In the undated image, the dog was wearing a specially made vest or harness.