Northland Saga: Regenerate and a one eared NPC (spoilers)

By the time the players have rescued the one eared Njal they'll soon have acess to Regenerate (and even if they didn't, they could grab a scroll on a trip down south). Normally I wouldn't think much of it (The PC receives 910 HS as a reward), but Njal becomes known as "Njal one-eared" latter.

 

Does it present any problem to allow it and just say the name stuck or do I need to pull "It's his wyrd"?