There is a good blog post on branding QGIS by one of the lead developers (Tim Sutton of Linfiniti) here - Building
Custom QGIS Installers for Windows.
It details how to customise the Splash Screen, and the title of the application. As underdark pointed out in her comment, you should be able to edit or replace all the QGIS icons and recompile to update this also.
To find icons you could search for all the images in the source folders and show them as thumbnails.
You may have received downvotes for wanting to "hide" the QGIS branding, but in my opinion and in the opinion of the developers, opensource should allow you to take and reuse code as you need it.
With all the flexibility that QGIS offers, being open source and 'out
there' for anyone to hack on, its easy to take what the project
provides and rebrand it substantially
- you can create a custom icon theme
- you can remove unwanted user interface elements
- you can replace help text, about text etc
- you can rename the application itself to something else
- you can change the application icon
But as Tim Sutton points out:
One thing you may not do is claim the fundamental work to be your own.
Any time you make a publically available custom version of QGIS, be
sure to remember that you need to redistribute the full source code
(including all your customisations) with it in order to comply with
the letter and spirit of the GPL.
A final point though - you may want to point out to the client that the development time used to brand QGIS, and then maintain your customisations as new versions of QGIS are released, may be better spent meeting their GIS rather than marketing requirements.