Hello ! I have LuckPerms 1.12.2 with VaultChatFormatter but the displayname isn't working.

Do you mean display name, or prefix/suffix? Because these are both entirely different things.

Also 1.12.2 is the server version, not the LP version

I mean displayname.. I don't know how to set prefixes/suffixes..

And the version of luckperms is:
LuckPerms-Bukkit-4.4.1

VaultChatFormatter doesn't change the displayname of the player. It is only for adding prefixes and suffixes and for basic chat formatting (setting colours)

You need another plugin like EssentialsX and EssentialsXChat to display the displayname.

The wiki is your friend: https://github.com/lucko/LuckPerms/wiki/Prefixes,-Suffixes-&-Meta

Ok i Will set the prefix when i'm back To my home. I Will inform you for the advencement

Ok it's working ! Thank you for the support !