Status Updates From Dashiell Hammett Collection

"The girl looked at the place where he stood as if no one stood there, as if, in fact, no one had ever stood there, turned her small back on him, and walked very precisely down the street."

"Why, he wondered, whenever there was some special reason for gravity, did he always find himself becoming flippant?"

Some of these short stories are about a continuing character who is never named. I've read three (or maybe it's just two... hard to tell for obvious reasons) where the only thing we find out about the point of view character is that he works for the 'Continental Detective Agency' and he's well known by the police department.

Could a writer get away with this today?