If I select a demigod, then expand the text box containing their description and backstory, when I collapse this text box the Random Assassin image (purplish blob with question mark) will appear overlayed on top of their animated model.

Similarly, if I select a Random Demigod or a Random Assassin/General, then do the same thing, the animated model of the previously-selected character will appear behind the Random image.

Backing out of the character-select screen and reopening it will return it to normal, as will switching my selection between a character and a random selection a couple times.

This only seems to occur where you actually have the option of choosing a random demigod, i.e. in Custom Game lobbies and single-player Skirmish lobbies.  It does not occur when selecting a demigod for online Skirmish or single-player Tournament.  Not sure about Pantheon or LAN lobbies because I have not tried it in them, but it's likely dependent solely on whether the Random Demigod option is available.