canada
I am aware of no case raising this fact pattern. However, much has been said about defamation where the plaintiff is not explicitly identified.
To be successful in defamation, the plaintiff must show that the published expression "would tend to lower the plaintiff's reputation in the eyes of a reasonable person" and that the published expression "in fact referred to the plaintiff" (Grant v. Torstar, 2009 SCC 61 at para. 28).
When the plaintiff is not named, the question is whether there is evidence from which an "ordinary sensible person would draw the inference that the words referred to the plaintiff." That evidence must "connect the [defamation] with the plaintiff." The plaintiff needs to show that it would be reasonable for a "hypothetical sensible reader who knew the special facts" to infer that the impugned expression referred to the plaintiff and that these special facts/circumstances were known in the community. See S.G. v. J.C., 2001 CanLII 3041 (Ont. C.A.) at para. 24; Arnott v. College of Physicians and Surgeons of Saskatchewan (1953), [1954] 1 D.L.R. 529 (Sask. C.A.) at para. 70).
For an argument that it should be possible for the person behind an avatar to sue for damage to the avatar's reputation, see Mark Lemley & Eugene Volokh, "Law, Virtual Reality, and Augmented Reality" (2018) 166:5 U. Penn. L. Rev 1051. That article is based in U.S. law, but I don't see their argument on this point to be limited to that context, given that is largely an argument from policy and first principles, rather than one based in legal doctrine.