A player can belong to the right group and still have an empty rank label. First check that LuckPerms actually resolves a prefix for that player in the relevant server or world context.
Find the value TAB displays
When TAB and LuckPerms run on the same instance, TAB can read the built-in %luckperms-prefix% placeholder. Merge the example into the existing DEFAULT block in groups.yml.
_DEFAULT_:
tabprefix: "%luckperms-prefix%"
A player, group or world-specific tabprefix can override the default. Check which setting applies to one test player. Reload TAB and inspect the player list with that account.
If TAB runs on the proxy and the metadata exists only on Paper, configure the supported bridge and backend placeholder described in the TAB docs. Check chat and the overhead nametag separately.