I've checked both stories in which the kryptonite pooch appeared---from Superboy # 83 (Sep., 1960) and # 99 (Sep., 1962)---and I don't find a name given to him.
The first thing I thought of when I saw this topic was The Kryptonite Kid, the 1979 YA novel named a "Best Book for Young Adults" by the American Library Association. I didn’t hear of this unusual novel (written entirely as letters to Superman) when it was new, but I found it on the book trade table in my workplace circa 1992 or so. From the back cover:
This unforgettable novel, at once touching and funny, presents Jerry Chariot, an ordinary American kid who writes letters to Superman, because Jerry really believes in The Man of Steel. He is a boy who years to be loved and yearns to be Super in an everyday world so filled with unfairness that he must create his own reality—until the book’s shattering conclusion makes Jerry realize who Superman really is.
Despite what one of the reader/reviewers on Amazon.com thought (which 1 of 46 people found helpful), I think it is a good novel for young teens to read however that all the references to Silver Age Superman stories are so dated that no one under the age of 40 is likely to be able to relate. I always meant to read it a second time (and will someday), and do recommend it as a light entertaining read for those familiar with Superman of the Silver Age.
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This unforgettable novel, at once touching and funny, presents Jerry Chariot, an ordinary American kid who writes letters to Superman, because Jerry really believes in The Man of Steel. He is a boy who years to be loved and yearns to be Super in an everyday world so filled with unfairness that he must create his own reality—until the book’s shattering conclusion makes Jerry realize who Superman really is.
Despite what one of the reader/reviewers on Amazon.com thought (which 1 of 46 people found helpful), I think it is a good novel for young teens to read however that all the references to Silver Age Superman stories are so dated that no one under the age of 40 is likely to be able to relate. I always meant to read it a second time (and will someday), and do recommend it as a light entertaining read for those familiar with Superman of the Silver Age.