I just did this successfully on my 2012 Mac Mini and 2020 MacBook Air, both running Catalina. I found what I wanted to use as the icons as png files (one was originally a different format so I had to convert it first). I opened the png in Preview, copied the graphic to the clipboard, did Get Info on the drive icon I wanted to change, clicked on the little icon at top-left of the info window, then pressed Cmd-V for paste. I think I was prompted for my password, entered it, and I had the icon(s) I wanted. (I did this because I use a 27" monitor at times for both computers, and having the drive icon displaying on the desktops, and looking like the actual computers, helps avoid confusion about which computer I’m seeing. Yeah, I could use different wallpaper, but, well, I just like the wallpaper I’m using on both of them.)
Hope this is helpful!