By “inscription” do you mean the letters “INRI” (Iesus Nazarenus Rex Iudaeorum)? It is perfectly fine for a crucifix not to have that on it. There are many styles of crucifixes.
If you mean the corpus (body), there’s nothing wrong with a plain cross. It is found throughout traditional Catholic architecture, and in Carmelite monasticism a plain cross is used to represent that it is your cross. That said, a plain cross cannot replace the altar crucifix in a Catholic church or chapel, at least not during Holy Mass.