[Hookbill the Goomba]

I could be wrong but my guess is that the initials are those of Christopher Tolkien. JRR was calle John Ronald Ruel (hope I@ve spelt that right) so perhaps the J and R of the initials on the map are Christopher's middle names, after his Dad

Christopher John Ruel Tolkein.

So yes, and I think that was the assumption made. If my Tolkienology is correct, he would have been the only Tolkien child still at home if not getting ready to leave home at the time of the end of writing The Lord of the Rings..

But here is the official line taken from My one volume edition of The lord of the rings;

Note on the maps

Maps accompanying The Lord of the rings were drawn by Christopher Tolkien for the original published in 1954-5. They consisted of a general map of the western regions of Middle Earth and a large more detailed map of Rohan, Gondor and Mordor; printed in red and black on large folded sheets pasted in at the end of each of the three Books. The Fellowship of the ring and The two towers carried the general map, while The Return of the King carried the other. In addition, there was a map of the Shire in red and black preceding Book one. Christopher Tolkien redrew the general map expressly for inclusion in Unfinished Tales (1980), but subsequently this replace the original form in editions of The Lord of the rings.