Is there any module to create different menus per user? I would like to have different menus per user.

How can I achieve this?
I searched on drupal.org, but I found a module that creates a menu per role, not per user.
Yes. You can try OM Maximenu. It is really flexible and this means you will need some time getting the configurations right but it's really good especially when it comes to controlling menus per role.