Greater Daemons are not "marked" units, same thing with Daemon packs or daemonic beasts.
What you do is designate a single aspiring champion to be the daemon host for the Bloodthirster, he has no bearing whatsoever on which units count as troops, that is what your chaos lord or lieutenants mark is for, if you arent using a lord or lieutenant then you use the mark of chaos worn by the daemonhost, which in the case of the Bloodthirster, can be Khornate or Undivided.