this probably needs  discussion. you are merging the layer on top to the layer below so it is logical to keep the name of the layer below.

Sure, you are right. It actually doesn't matter in most cases, but there are situations when you draw a character for example, for cutout animation or game, you make multiple layers with specific names (lower arm, upper arm, ...) and initially you draw lines with this names for easy work, then you color this elements in layers below (base color layer, details, shading .. or something like this), and after this you have to merge them, and all the initial names disappear, and you have to rename it again.
I am not talking about changing existing logical method, but about option of merging operation.

Hi Stepan,

Yes, this is the type of situation where sometime one want to keep the name of the layer of the top while merging down. I think it is fair to tell it happens to everyone more or less rarely.

That being said; the default behavior "to merge down" is more logic: the layer on the top get merged on the one of the bottom on a compositing point of view. So it is most likely reasonable to let the layer of the bottom dictate most of the properties of the result, including name.

I'll give here two workflow where the merge down works well for default:
You have layer "Pencil", you create a temp layer on the top to create set of lines you can move freely and rotate on a "Layer 12" type of autogenerated layer name, then you merge down to bake this changes and it auto-inherit the "Pencil" name. Same with painting and paint over, or photo bashing over a "texture" layer and then merging all down into it.

I read your issue and the example are really specific; in my opinion they can be solved at creation of the stack with starting with properly named groups: then you can base color, ink, post-fx any body parts and keep the name of the groups during the full process while adding layer up or down.

That's why all in all, I wouldn't even advice an option. I hope you'll understan d.