I'm running MacOS 10.15 (Catalina). I looked through the settings of SourceTree but didn't see any options to change the icon/upload my own icon. Any help would be greatly appreciated!!
Solved! Type this line into Terminal.app:
perl -i -p -e 's/Pridetree/Bridetree/;' /Applications/Sourcetree.app/Contents/Resources/Assets.car