When you try to set an entity that isn't a player's score in the belowName slot, it doesn't show. This could be intended, but it's much more likely that it just hasn't been realized.

What I expected to happen was...:
I expected that when I set an armor stand's score (e.g. I set it to 3) and then set that objective to display below name, it would show the score below the armor stand's name.

What actually happened was...:
Once I set the score and set the objective to display below name, nothing showed.

Steps to Reproduce:
1. Summon an armor stand named 'Test' using this command:

/summon armor_stand ~ ~ ~ {CustomName:"Test"}

2. Create a scoreboard objective, we'll call it 'score:'

/scoreboard objectives add score dummy Score

3. Set our armor stand's score to 3:

/scoreboard players set @e[name=Test] score 3

4. Set the objective 'score' to display below name:

/scoreboard objectives setdisplay belowName score

5. (optional) Set the armor stand's score to 5 (just to make sure):

/scoreboard players set @e[name=Test] score 5

I really do hope that this is added, because it could help a lot of map makers.