No, I have don't have any numbers or letters of any kind.
My cue came from the estate of Bob Man. I never met the man, but he certainly had a huge inventory of the finest, most historical and most expensive canoes and paddles ever made in the last 60 years. Maybe he had Patrick Moore make something custom for him without a serial number. Of maybe he just didn't want inked numbers on his paddles. He took the label off his straight ZRE with symmetrical grip that I bought, or ordered it without the loud ZRE label.
He did put red and yellow tape on under the grip of many of his paddles, at least on the two composite ones I bought and many of the others I saw. I was going to remove the tape, but I've decided to leave it on. An outstanding canoeman put that tape on for reasons known unto himself, and it will stay there in his honor.
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Almost forgot,
@gumpus, you say your paddle is gray but there is no such color mentioned on the color pages of Pat's archived website. Is yours not Atlantic Blue?