How to get a term from the translated term name? I have a translated taxonomy term whose name is Autos Y Motores (Spanish). How can I get the taxonomy term object from it? 

If the term name were in English, I would use taxonomy_get_term_by_name('Vehicles &amp; Motors') to get the taxonomy term object. 

How can I do with a translated taxonomy term name?
You can try to translate it before pass it to taxonomy_get_term_by_name function, try some thing like

$string= 'De Lema'; // string in not default site language I suppose in French
$default_lang_short = 'un'; // I supposes you default site language is english change it to your default
$en_value = t($string, array(), array('langcode' =&gt; $default_lang_short));
taxonomy_get_term_by_name($en_value);