Here's a summary of the issue:

Merging Layers via Menu Bar Layer Option

Merge Visible: Merges visible layers (those with eyes turned on)
Gives name to the merged result as follows: If background is visible, uses name “background” under all conditions. If background is not visible, uses name of (1)Selected visible layer if only one layer is selected, (2)Topmost selected visible layer if more than one visible layer is selected, (3)Top visible layer if no visible layers are selected.

Merge Down: Merges a highlighted visible layer with a visible un-highlighted layer immediately below it. This will not appear as an option unless one and only one layer is both visible and highlighted AND the layer immediately below it is visible but not highlighted. (If the layer below is visible and highlighted, “Merge Down” disappears as an option and “Merge Layers” replaces it.) Gives the merged result the name of the lower of the two layers.

Merge Layers: Merges two or more highlighted layers if any one of the highlighted layers is also visible. Other highlighted layers if hidden (eyes off) will be merged in their invisible states, i.e., deleted. This option is grayed out if less than two layers are highlighted. The merged result gets the name of the topmost highlighted layer even if that layer is hidden and therefore deleted in the process, which is deceiving.