Some themes let you set logos via theme options or the WordPress Customizer. To add different site logos for the different languages of your site, you need to tell your theme which logo to display in each language.
To do this, get the IDs of the logos you want to use in your default and secondary languages from Media > Library.
Then, go to WPML > String Translation and search for the default language ID.
If you can't find it, click on the Translate texts in admin screens and add the string to the String Translation table. Add the secondary language ID as the translation.
