NYD, in my opinion, removing the labels takes the emphasis off the product and puts the spotlight on you, the detailer. If they are a car enthusiast and really want to know the products you use, terrific. More than likely, the customer doesn't want to know what you used on the trim around the window vs. what you used on the rubber seals around the door. They want their car to look new again and you are in the profession of doing so. Yes, this does include paint correction in lieu of a suggestion to take it back to the dealer.
I don't ask the surgeon what brand of scalpel he uses nor do I ask the maintenance man what brand of vacuum he uses after office hours. If I am alive and kicking after my surgery and the floor looks great every day, I congratulate the facilitator. If I pat the maintenance guy on the back, I don't want to hear "Hey, wasn't me, man--thank the Oreck!"
The sense of mystique to the client is reason enough to support your label removal. Concealing detailing recipes from your "friends" (who would steal product from you) is merely additional benefit. As a detailing professional who will have been in the business 20 years 19 years from now, I understand your reasons for taking naked bottles with you on the job.