In here you can change the colors, add additional logos etc.
As I mentioned, your mileage may vary, and just because you’ve changed one part of the file, doesn’t mean the style/image is being set elsewhere.
I think it would be worth you submitting an idea for there to be some basic out of the box styling to quickly facilitate different environments - https://community.safe.com/ideas
If you don’t want to get into the backend code like @hkingsbury and I like to do. You can always create a broadcast message on the home page.
It certainly is not as cool, and won’t show up in server apps, where changes to login and internal logos flows through to everything. But it is certainly quick to implement.
Or you can replace fme-logo.png in <FMEFlowDIr>\Utilities\tomcat\webapps\fmeserver\images\
But you would need to make sure it is the same size, otherwise you would need to change other css files.