When you view the list of Processes in Task Manager, each entry gets a little icon. Where does that icon come from?

If the process has a visible window, then Task Manager uses the icon of the window.

If the process has no visible windows, but it has a notification icon, then Task Manager uses the notification icon.

If the process has no visible windows, nor does it have a notification icon, then Task Manager uses the default icon for the underlying executable.

There is also a special hard-coded list of icons for certain processes, such as svchost.exe.

A customer had a process which showed only a notification icon most of the time, so they ended up at step 2: Task Manager uses the notification icon. Their notification icon was designed to look good against a dark background (which is the default for the notification are), but it looks bad on a light background (which is the default for Task Manager). They were hoping for a way to specify a custom icon just for Task Manager.

Sorry. There is no custom override just for Task Manager. Maybe you can tweak your notification icon so it looks good both in the notification area and in Task Manager. You probably should do that anyway, because the background color of the notification area will not always be dark; users can customize it to something light, and now your notification icon looks bad everywhere.