My class is currently doing this text, and it doesn't seem too bad, but I interpreted it as Moon and Huck and Puckeridge having transient identities which represent a complexity sorely lacking in the works of Agatha Christie and her characters which are more like cardboard cutouts. If you mean in the physical sense who they are, well Higgs is the original critics who became the dead body seen at the beginning, while Moon replaces him as critic (his understudy so to speak), Moon eventually gets caught up in the play becoming the Inspector and dies, being shot by Magnus aka Puckeridge(Moon's understudy).
Also may I ask for the details of this performance of the Real Inspector Hound?