This technique should work with most applications in Linux Mint. If you are using a different variety of Linux, you may have to adjust the exact steps.
Dolphin file manager is excellent. Two panels for easily copying or moving files. Multiple tabs to have file listing of multiple folders. Save the current tabs and panels when you exit. No more having to tediously browse to your favorite folders. Open your Terminal in the current folder.
But the Dolphin icon uses the identical icon as the default Mint file manager. While there are a few things where I need to use File Manager (Nemo), I do want to have icons where I launch the program I want.
Edit the Application Menu
Right-click on your Start icon. (It’s the icon you’d click instead of pressing your Windows or Apple Clover key), select “Edit Menu”.


Click on the Properties button. From there, click on the application’s icon in the top-left corner. Select whatever icon you like from the list. (I used the existing “add-files-to-archive-symbolic” icon.)
How to Add Icons to the Icon List
I don’t know yet. I looked up “linux mint change an application icon” and there are many sites explaining how. You can install an icon that you made, in formats like svg or png.
Then I got distracted looking at sets of icons that you can install, and many of them look pretty, but didn’t see any where I could install a single icon.
Tip: drag the top of your Start menu up, and you can see more icons in the left-most edge.

The changed icon shows in other places, such as the Alt-Tab menu and the bottom-of-screen Applications list.