As of since at least 18w49a, the boss bar does not show up if your render distance is below a certain value, dependent on your distance to 0/0, which can cause trouble if you don't know that when testing for this bugpost.
It was not the case in an older snapshot version.
This does apply to naturally spawned as well as summoned (via commands) dragons, even if you're in their direct vicinity.

See also this comment

Several EnderDragon issues, I don't know if anything relates to each other, thus I'm listing them all: MC-105976, MC-105980, MC-105981, MC-105983

4a) When I tested boss bars in the first 1.11 snapshot, I noticed that only one EnderDragon has got a Boss Bar.

When I summoned a second dragon with the command

/summon ender_dragon ~ ~ ~

it didn't have any boss bar, also after relogging into the world.

Are we not going to have several boss bars for several bosses?

When all dragons in The End are dead and I use

/summon ender_dragon ~ ~10 ~ {DragonPhase:0}

(the new summoned dragon moves and) it still doesn't have a boss bar rightaway.
Upon relog the command-summoned dragon does have a boss bar again.

4b) Dragons in the Overworld don't have a boss bar even upon relog.
It'd be great for the mapmakers to have dragons display their boss bar also in the Overworld, not only in The End, if possible code-wise.
If not, we'd be restricted to EnderDragon boss bars only in The End and could solely be using Wither Bosses in other dimensions.

(I think this is technically a new bugpost?
I can't find an issue regarding that (something like: "summoned Dragon (via command) does not have boss bar in the Overworld, only in The End"), but I'm unsure if I shall post it separately, if I shall make a new bugpost for that, please tell me.)

Side note: a CustomName does work for EnderDragons in the Overworld, it shows up above them in the Overworld, just not as boss bar.
In The End the dragon does have a boss bar with its name, even if there are other Dragons in another dimension, e.g. the Overworld.
However, also in The End, the CustomName-boss bar only appears after relog.

Example command for a dragon with a custom name:

 /summon minecraft:ender_dragon ~ ~10 ~ {CustomNameVisible:1b,CustomName:'{"text":"Liebling"}'}

Attached pics for proof, dragon in The End as well as Overworld are both in the same worldsave (and alive at the same time).