Rule "Res-Alloc" in documentation is stronger than the Coq version
In the rule "Res-alloc" on page 26 of the documentation (see https://plv.mpi-sws.org/iris/appendix-3.1.pdf, or https://gitlab.mpi-sws.org/FP/iris-coq/blob/master/docs/ghost-state.tex#L211) the set for the new ghost name is allowed to be an arbitrary infinite set.
However, what's proved here (https://gitlab.mpi-sws.org/FP/iris-coq/blob/master/theories/base_logic/lib/own.v#L116) in the Coq code is a little bit weaker -- you only get that the new name must be in the complement of a finite set.
The stronger rule should be true though. As @robbertkrebbers points out, basically one first needs to port something like
gmap, and then the stronger result follows.