Shouldn't I be concerned for Nineveh, that great city, in which are more than one hundred twenty thousand persons who can't discern between their right hand and their left hand; and also much cattle?"
It was certainly not out of keeping with their national custom to hold a public funeral for "deserters," bury them in effigy, and engrave their names on a grave.  It is our speculative opinion that they surely did this for Jonah, and that that is how his name was ever found on a grave in his home community.