Are these correct sentences and can they be with or without "by"?
A child is someone who can call a duck a goose.
A child is someone who can call a duck by a goose.
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
The first is correct. The second is not.
Ordinarily I would try and elaborate this answer with some attempt at creating a similar, but valid, sentence featuring "by", and explaining the difference in meaning from the first. However, in this case I can't envisage any similar sentence with "by", so I'm afraid I can think of nothing further to add.
You can call a duck a goose.
You can call a duck Henry
You can call a duck by the name (of) Henry
You can call a duck by the name of a goose.
You can call a duck by its own name, or by your brother's name.
You can call a duck by a rude name.
So call ... by ... is used only when what follows the "by" is phrase that contains the word "name". (Probably also with a synonym of "name").