I have just had both my Airpods Pro (left and right buds) replaced under warranty, and now they show up with a "1" as the serial number in the iPhone and iPad Pro settings screen.
I found another thread in here discussing this same issue back in November 2019.
I contacted Apple support, and after spending some time talking to a person who didn't seem to know anything about Apple products, she eventually transferred me to a supervisor who said he knows about this and that it is expected behaviour showing them that one or both of the Airpods 2 or Pro have been replaced by Apple.
I advised him that I am dissatisfied with this because it reduces the resale value of the Airpods Pro, as checking the serial number in the settings is one way to check that they are genuine articles.
He advised me - as you would find people in this forum also advise you - to submit this via the apple website feedback page. I have gone ahead and done that.
In my opinion, if Apple are replacing a pair of iPads Pro under warranty, they should just replace the whole lot as a matched set; case, and left and right buds all together with a working serial number in settings.
Or, if they continue to just replace the buds individually while the owner keeps the case, as the unique serial number is on the case, that serial number should still display in the settings app. I don't like the way it works currently. I had to have the nearly new earbuds replaced through no fault of my own under warranty (they were both exhibiting a loud buzzing sound when there were loud external sounds after updating themselves to firmware 2D15), and now I have to live with a non matched set that always shows in settings incorrectly.
Ideally, the settings app should list all three serial numbers; the case one, and the ones for both the left and right earbuds, since Apple treats all three as separate entities - rather than as a set - post-purchase.
(To the standard repliers who reply to every forum post saying "Apple don't read these posts, post your comments on the feedback form", please don't do that; I already have posted my comments on the Apple feedback form.)
