Here's a little test project to show you how I'm doing it. Note that it prints the type and name of the Player object. However, I'm doing the print in _ready(), and at that point I can be sure that all the nodes in Player at least exist. The scene tree is loaded in a particular order, and children are initialized first, so that order may be foiling your attempt if you're setting player too early. I'd set it in _ready(). Also, I'm assuming a lot about the rest of your project, since I can't see it. When you test what you've got now, make sure you're running the game (F5), not the player scene (F6).
Edit: You can look at the actual scene tree by clicking "remote" in the scene tab, to make sure everything is being placed and named correctly.