Hello Samer,
You are right that the site name will be added in the logo image as the alt text but alternative text value does not function the way you described.
Please check this link to read more about it:
https://www.w3schools.com/tags/att_img_alt.asp
What you are looking for is the title attribute which is not present in features of the theme but a quick solution would be to make use of Javascript to add the title attribute to the logo image. Please add this code in X > Theme Options > JS:

jQuery('.x-brand img').attr('title', 'You title text');
Kindly note that since this is a custom code that changes the default behavior/display of the theme, you will be responsible to maintain or update the code in case you require further changes or if the code stops working in future updates. If you are uncertain how to proceed, it would be best to get in touch with a developer.
Hope this helps.