My bitsa has an American Special Jazz neck with, obviously, a Fender Jazz decal on it. I've certainly considered having that changed to a Precision decal. But my previous Squier bitsas were left badged as Squier. It was always great to see people's reactions when they played these, they were way better than expected, every time. So why bother to swap?
However, I did put a TV logo on an otherwise bare Allparts neck that my bitsa previously wore, as blank was too...blank.