That does sound vaguely familiar. Jeff did have a handful of other "name candidates" sitting around, and this seems like one in keeping with the sort of thing he was thinking about. I don't specifically remember it though.
There are a couple of institutions in the Seattle area that have pretty good generic domain names, presumably because of the tech connections in the area. For instance, the Washington State Fair has the domain thefair.com.
"Bezos and his wife grew fond of another possibility:
Relentless.com. Friends suggested that it sounded a bit
sinister. But something about it must have captivated
Bezos: he registered the URL in September 1994, and he
kept it. Type Relentless.com into the Web today and it
takes you to Amazon." -- Stone, Brad. The Everything Store (p. 31). Little, Brown and Company. Kindle Edition.
N.B.: "Today", in the context of that quote, is ca. 2013, when the book was published. relentless.com redirected to amazon.com for me this morning (2021-02-03).