When you first bought the shares you would've received...

When you first bought the shares you would've received correspondence asking for your tax details (since it seems your share broker didn't automatically provide it to them - I use ComSec and it does it for me automatically, maybe it's a setting, not sure?)

Anyway, you need to log onto your holding on Link Market Services

You can try One Time login, that should be okay as well

Update your details as you require and it'll be all good to go then

The process of logging onto the share registry administering your shares in a company works for any and all shares.