How can I Add Different Banner Images On Mobile And Desktop In Shopify (Dawn Theme)

Store Design
3

You could give this ‘workaround’ a try.

Go to your Image banner section. Set two images; first image is for mobile and the second for desktop. Scroll down and add this Custom CSS,

.banner__media-half:nth-child(2){ 
  left:0;
  right:auto; 
  width:100%; 
}
@media(min-width: 750px){ 
  .banner__media-half:nth-child(1){ 
    display:none; 
  } 
}
@media(max-width: 749px){ 
  .banner__media-half:nth-child(2){ 
    display:none; 
  } 
}

Note. Set checkbox: Stack images on mobile.

My two cents. Good luck!