I'm pretty sure the ID that Discord and Blizzard use as the "true" source of identity (as in, the key they store in the database to keep track of who's on your buddy list) is different from the "#1234" number used to disambiguate people with the same username.

In particular, that number is only four base-10 digits long, and I'm pretty sure there are more than 10,000 people in the world who have ever played Hearthstone.