What do the residents call the newly born felt in the mysterious island?

The new felt is called "Lincoln Felt".

What you are talking about is the homemade felt made by five Americans living on a desert island (named Lincoln Island) using their knowledge and labor in Verne's famous science fiction novel "The Mysterious Island". Because it comes from "Lincoln Island", the islanders call it "Lincoln Felt".

See novel images below.

"The Mysterious Island" is a novel written by the French science fiction novelist Jules Verne. It is the third part of his trilogy. The whole book has three parts and 62 chapters.