I know they're joking around and he points out it's technically a fake name but I have been quietly feeling emotional about the spell names because it feels like he's kind of making a history for the name he has with the Nien. Like even if Caleb Widogast isn't what he considers his Real Name because trauma and such, Caleb Widogast is a member of the M9 and he's leaving his mark on history with the name he chose and the family he chose😭
As contrasted to how Veth was Nott the goblin. Caleb is Caleb. Bren is the person who got indoctrinated and mind controlled, and Caleb is the one who has to fix the mistakes, and try and do some good in the world.
Not meaning to nay say your head cannon (I like it), but for anyone interested it was Matt who started using those spell names in his guide to Wildemount and it's on DnD Beyond. As Liam is (was) our 'rules as written' President, he is honor bound to use the spell's official names.