f5 ASM tracking user - session_id attribute in logs are not unique

Do you want to track users who log in to your ASM-protected website using username/password? Do you have Login pages configured? In such case you should be able to track users by username from the moment they login till they log out using ASM. Check out this article on how to configure this feature:

https://devcentral.f5.com/articles/the-big-ip-application-security-manager-part-9-username-and-session-awareness-tracking

In case if you are talking about website visitors (e.g. anyone, not necessarily a logged on user) ASM will not help. You can do it using an iRule setting a tracking cookie. See this DevCentral thread for a sample iRule:

https://devcentral.f5.com/questions/visitor-session-cookie-without-persistence