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MacOS Monterey – not desktop icon, but icon for different RUNNING firefox profiles

Rather new to MacOS (monterey here) though I’m a linux guru for 2 decades, and a UNIX Guru from 3 decades ago. So my question might be trite.

Icons for items on the desktop is working for 2 firefox profiles. BUT when each are running, still see the usual firefox icon and name (“Firefox”).

I found How can I change an application icon in Mac OS X? but that just gives what I already have – desktop icons.

There are other superuser questions, but they are far out of date, and all links from those threads are 404. Any modern solutions?

Many thanks in advance.

[long time reader, first-time poster]