Is there a way to create underlay for player, which would appear under the player (1.), but over the tree, while the tree is over the player (2.)? :)

I hope this picture will explain better what I mean:
No. This situation is non-transitive and so the layering engine can't handle it. That is, there is no clear sort order. You want A > B > C > A: A being the tree, B being the player, and C being the underlay. The only way to solve this is to break one of the items into pieces so it's not one unit. We don't do that automatically because it's extremely non-trivial.

However you do have the option of making the ring and the name separate, and making the name an overlay that gets put on EFFECTS_LAYER. That should always keep it in the foreground.

Lummox JR