Code names have no relation to the plot, they’re just code names to avoid leaks and stuff. S1 code name was Willow Hill but you don’t see that in S1, S2 code name was Nero but he’s dead and only mentioned in 1 episode
"Pilgrim" was the production code name for S1 of Wednesday. It was all over everything BTS.
And we do "see" Willowhill (not "Willow Hill", like in this already inconsistent monster mash):
If Nero is/was the code name for the incoming train wreck, then you might want to consider that more carefully seeing that a pilgrim was indeed the OG antagonist and central to what Gatesmonster was doing in S1.