When the icon shape is round it might look like what you describe, have you tried changing the shape? Even the stock android launcher has that option I believe, but I might be wrong.
Edit: and if you don't like that it says F-droid in the name of the Fennec app, just rename it? Sorry, I might be misunderstanding you, but those reasons are a bit silly and easily fixable.
Long press on app icon. Rename. Maybe your launcher does not have that.
And that first screen. You see that a split second when the app starts, if something like this is a problem for you to use the app then you cannot be helped.
Can you edit this without pushing your own commit and rebuilding the app entirely?
You can't do shit because it's a problem with your phone. This is not something handled by the app. The app only provides the icon, it's Android that's supposed to handle the launch animation; that's why launch animations can look completely different on phone's made by different OEMs.
You mean the home page branding. Just change the home tab to a different page, problem solved. Might need to be done via about:config but it should be possible; I know it's possible in Mull at least, I had changed it a one point a few months ago when I was going through the config options and it worked.