Like Nichole, you used remind correctly.
You can also refer to it as 'my desktop wallpaper,' or sometimes even: 'On my desktop, I have a picture of a place that I used to work at because it reminds me of when I used to work there.' Just saying 'desktop' can be vague, but we usually know 'desktop' refers to a computer whereas 'on my desk' would more obviously be a physical desk.
You can say 'I put the picture as my desktop wallpaper,' but you can also just say 'I have a picture as my desktop wallpaper...' or also 'I set a picture of my former workplace on my desktop to remind me of when I used to work there.'