Note: this edit has since been made to the master release and should now ship with the latest install packages https://github.com/qgis/QGIS/pull/7309

 

I am a huge fan of QGIS and I agree with Nyall Dawson, in that the release of 3.0 has set the foundations for beautiful things to come and is an industry game-changer.

I have recently upgraded to 3.2 Bonn on Ubuntu 18.04 LTS (Bionic Beaver). The past few releases have shipped with an application icon that has a white background. If you are interested in editing the icon background transparency, which, in my opinion, looks a little nicer in the Dock panel, then, the following are a few steps that might help.

Out of the box the icon ships as an SVG file with a white background and looks like this:

and looks like this in the Dock:

 

To edit the background transparency, open the qgis.svg file, which can be found here:

/usr/share/icons/hicolor/scalable/apps/qgis.svg

Edit line 5 of the file from

<rect x="0" y="0" width="256" height="256" fill="#FFFFFF"/>

to

<rect x="0" y="0" width="256" height="256" fill="#FFFFFF" fill-opacity="0"/>

 

You should now have an SVG icon file that looks like this:

and looks like this in the Dock: