I’m assuming you’re using WordPress Full Site Editing and have a Site Logo in your default language template. This may work for older WordPress templates, but I haven’t tested.
First step is to upload your new logo to the media library.
Take note of the ID of the Logo in the media library. Hover over the edit link and write down the post id.
Next locate your original site logo image in the media library, take note of it’s post id as well.
Now go to WPML->String Translation. Scroll to the very bottom and you will see a link “Translate texts in admin screens »”, click that.
Now search for the id of your existing site logo. It should filter down to an option ‘site_logo’. Click the checkbox on that row and the Add to String Translation button.
Now back to String Translation, search the id again. Now it should be translatable. In the translation, put in the id of the new image you uploaded.
That should do it.