Strider Said This Strider Did That

[Morsul the Dark]

As we all know Strider was once a Hobbit.

I'm curious if there's any evidence when this change occurred?

I'm asking because listening to Fellowship again there's a narrative quirk. In book one Tolkien calls him Strider (Strider said this Strider did that.) it's not until book two the Council where he becomes Aragorn in narrative.

I see three possibilities.

A) Tolkien wrote Strider as a Hobbit changing his mind at the council, adding a letter from Gandalf and some minor tweaks he doesn't have to change much.

B) he decided it wasn't until Aragorn's full stature is revealed in Rivendell that he "became" Aragorn in Frodo's mind. (This is a bit of license to the idea the Hobbits wrote the book).

C) just a narrative quirk nothing more.... boring.