while i'm on the topic, i love that chuck's death book is labeled with thee greek letters alpha and omega. talk about detail. alpha and omega as god's name, in that context? insane.
it's a biblical reference, a name of god from revelation 22:13: the alpha and the omega, the first and the last, the beginning and the end.
the first (and only other) time this is directly referenced in spn is the s11 finale, iirc, which is titled "alpha and omega". in that episode, chuck almost died, but dean got through to amara and convinced her to make up with her brother. why did they call that episode "alpha and omega"? it likely refers to chuck and amara in a kind of divine dichotomy way -- chuck as beginning and amara as end -- but does it really? biblically, god alone is alpha and omega. i don't think the episode title refers to amara at all, at least not the way we think. dean (chuck's favorite puppet) convinced amara to save chuck without chuck having to change or sincerely admit wrongdoing at all. chuck and amara left together, acted together for the first time in eons, with chuck calling the shots as always. the ending of s11 definitely wasn't "family therapy" like so many people seem to say. i think chuck conned amara in s11, and the ambiguity of the finale title only makes me more convinced of that.
then, of course, we have chuck's death book in s15.
to push another of my little theories, i think amara doesn't have her own death book because her fate is tied up with chuck's. her death book is chuck's death book. in that sense, alpha and omega is a duality, their cosmic twins duality, but that duality is always subsumed by chuck. amara basically says so in 15x15. she tells sam and dean that she and chuck "are the same" and were one at the beginning of everything, which is how they end up in 15x17.
again, i also think the death books are something chuck controls. we never hear about them until billie replaces the original death -- a result of dean and cas' actions, a result of chuck's narrative. she sings o death in her introduction, marking her in a distinctly meta way. billie has always been one of chuck's toys. later, so is betty. the library, the books, they're just narrative, and chuck's book is the icing on the cake.
his book, titled the beginning and the end! his book, according to which death formulates her plan that turns out to be chuck's plan and makes the characters say things like "we have to, it's in chuck's book"! his book, that says "in the end there is the ending of he who created the beginning"! chuck's ending, not his end!