He’d probably just check in with higher-ups if they were actually legit; I have a headcanon that every Ebon Knight is “registered” in Acherus as a way of distinguishing them from Scourge and as a form of accountability for any actions they take. If they’ve not made at least some attempt to get in touch with them, even if they never associate with them afterward, they’re considered a rogue death knight and a potential Cult of the Damned operative.
So he’d not do anything outright hostile because he knows the Lich King’s death let a few break free, but he might try to find out who they are because the last thing the Horde needs is someone doing covert Scourge work in its ranks. The enemy of his enemy is not, in fact, his friend.
(I don’t know if they actually make DKs register their name in a ledger. They did in the Scourge; I just assume it’s a carry-over habit for the sake of safety. Blah blah headcanons.)
Even if the Ebon Blade didn’t, which really doesn’t make sense considering they’re technically an Order so they’d be fairly rigid in actual structure, the Argent Crusade would. There’s a reason that Acherus floats right near Light’s Hope Chapel and it’s not so they can mope about all the dead Scarlets.
tirion’s signal is actually just another statue of himself