I tried to use the texturepack, that allows to name an armor and change it texture. The texurepack clearly works, but when you put on a named armor, it doesn't display. Even though regular armor texurpacks work fine. It's not the problem of this particular texturpack, as I tested other 2 familiar ones and all of them don't display.

I also tried to turn on smart animations, and noticed that named armor doesn't work only with fighting animations.
(here i use two texurepacks, the described one and regular texturpack that changes netherite armor texture)

Important note: the texturpack i described requires Optifine to work. I have custom items setting on though. If a problem concludes in different model type, than it used in the mod, how can i convert the texture to a necessary format?

same, this happened on new default + too. or every texture that has renamed armor. and i tried dungeon gear (its a mod) its didnt work too. so i hope it will be fixed very soon

Hello! and sorry for late reply. All optifine texturepack bugs are figured out as unfixable since I don't have a right to access to optifine code. Thanks for wait and sorry again.

ACTUALLY, you can do that with Custom Model Data, please try it and show me the results xD

Could you try remaking that texturepack but with CEM from JEMs ?
https://www.curseforge.com/minecraft/mc-mods/json-entity-models-jems
(edit: forget this they didn't yet add support for custom nametags)