The bug
Most Survival-obtainable items with non-white name colours have this aspect defined through the rarity system. Ominous banners do not, which is the root cause for some inconsistent behaviour when compared to items using rarity:
MC-132201: items with rarity don't display name colours in shulker box tooltips; ominous banners correctly do
MC-249067: ominous banners lose their name colour when renamed, which does not happen for items with rarity
Steps to Reproduce
Obtain an Ominous Banner
Run
/data get entity @s SelectedItemwhile holding the Ominous Banner
Observed Behavior
The color field is used in the item_name component to specify the Ominous Banner's name's color.
Expected Behavior
The rarity component is used to specify the Ominous Banner's name's color.
How to fix
Introduce a dedicated rarity for the ominous banner and apply it.
The Ominous Banner could be given the Uncommon Rarity like Bedrock Preview 1.21.30.22.