How to get taxonomy term reference fields value translated in twig
Maybe I poorly explained the question but the solution was possible without preprocess.
In a content type, the referenced field with a taxonomy is called field_lorem
For this Entity reference field (Type of item to reference : taxonomy term), we select in Manage display (admin/structure/types/manage/content_type_name/display) « Rendered entity » instead of Label :

In the node template (node--lorem-ipsum-content-type--full.html.twig), we have simply {{ content.field_lorem }}
Then, we are able to see twig suggestion template name for this field based on taxonomy_term.html.twig :

In this twig, we can style independently all of the fields of the taxonomy term :
    {{ content.field_image[0] }}

    &lt;p&gt;{{ name[0] }}&lt;/p&gt;

With this solution, translation of vocabulary terms works and we are able to have a custom template with all the field (in example an image field and name of the term)