I find myself frequently rebuilding bikes rescued from trash. They usually get stripped of parts, sanded down and rattle-can'ed (but I'm now a confirmed powdercoat fan), and rebuilt with newer parts. Then I typically give them away --sometimes back to the original owner, but more often to neighborhood families or college kids.
So now I'm feeling a little guilty for having removed the identity of a couple reclamation projects (Mercian frame, Nishiki frame, Trek820 frame, and more) where I made no attempt to restore/recreate decals or reattach headbadges.
I am restoring a Mel Pinto tandem now (newly powdercoated) and may try to recreate the logos. I also have a Viscount Grand Touring frame, and a Schwinn Crosscut full bike scheduled for new paint and build ups. Part of me says to relabel everything as close as I can, so the next owner knows what he has (I do these up expecting them to last indefinitely). But it would never be a total original restoration, so is it really worth it?