As of 23w41a, it was stated in the change log that ''The name of non-living entities will now be shown if looked at and a CustomName is set, or always displayed if CustomNameVisible is set, similar to living entities''. This fixed MC-249408 and made it so boats show their name if named, but it does not apply to Armor stands, which are a non-living entity.

Also worth noting that on Bedrock Edition Armor stands show their custom name when placed. Although this is an older feature and does not apply to the current parity rules, its still worth mentioning.