The template expression $object.main_node.name returns the name using the *default language* and to the currently active language.

Thus
{{
node.name != node.object.main_node.name
}}

Steps to reproduce

Two languages are defined: IT as default and EN as secondary.
An object is created in the default language and a translation is added.

The value $obj.main_node.name returns the main language translation (IT, in our case).