Update:
If you want to display a random image on button click this option is better:
Place an image and make it a list. Max items: 1
Place an input field
Place a random picker
Image list filter: Name contains input value (it is important to select contains. I tried with equals and it didnt work)
Random picker set up:
Collection : Images (or whatever. Basically the same collection as the image list above)
What happens when user clicks on component?
Pick a new item
Action after refresh:
Update input: Value: Current item’s name.