Some cars I've left the nameplates on, others I've had removed at delivery. Dealer plate frames usually go right in the garbage when I get home.
However, I have noticed that it sometimes affects service.
If you always visit the dealer where you bought, you probably won't notice a difference.
But take it to a another dealer with a different dealers nameplate and you may find a different level of service. Some will go farther to please you, so that they take the service business away from another dealer. Some don't do anything extra for you since you didn't buy the car there.
A few years ago, one dealership said to me: "Our loaner vehicles are reserved first for customers who buy their car from us. If we have any loaners left, we'll let you use one." They used plate frames.
YMMV