Bug Report

Type /ver NametagEdit and post the output.
4.5.8

What version of Bukkit/Spigot/PaperSpigot are you using? Type /ver

PaperMC git-Paper (1.19)

What plugins are you using? Type /plugins
Plugins (31): AntiCooldown, AntiRain, BetterDeathScreen, BisectHosting, ccInstantRespawn*, ChatItem, Citizens, CitizensGUI, CommandDoesNotExist, DecentHolograms, Essentials, EssentialsChat, floodgate, Geyser-Spigot, GroundItems, JukeBox, LaggRemover, Multiverse-Core, NametagEdit, NoteBlockAPI, ore-control, Orebfuscator, PermissionsEx*, PlaceholderAPI, ProtocolLib, ServerListMotdSpigot, SimpleGeyserVL, TubeTils, Vault, WorldEdit, WorldGuard

Please explain your issue. How do you trigger it?
This happens when you are using Geyser (I think), or some sort of cross compatible feature. Anyway, if a java account joins the server and then a Bedrock account joins the server, it'll display the name tags accordingly. If the Java account relogs and rejoin (Bedrock will still be able to see it, so no issues). However, if the Bedrock client rejoins or just idles out then joins back (and the Java account stayed in the server), then the Bedrock account will see a normal white username for the Java account. Java side everything is working. Just a slight confusion for Bedrock players. To fix this maybe force reload on_join (not sure haha).

Another idea could be to add a "RefreshTagOnCombat" then a cooldown for it so it doesn't spam. I don't know just putting it out there. The main issue is ranked players aren't getting what they paid for.. "fancy rank above name" haha.

Are there any errors in the console? Please use: https://pastebin.com
Nope.

EDIT
Whenever any Bedrock account rejoins and joins back they'll also have no custom name tag to other bedrock clients.. But Java can see those.

Hum, that's an interesting issue, however NTE is designed to work with Minecraft Java Edition specificities.
For your information, a reload doesn't even work. Something Bedrock's side or a geyser limit, not easy to determine the cause 😅

Its probably not a NameTagEdit bug but a Geyser one (probably a wrongly translated packet)