ISSUE 1:
Started by user anonymous
That does not mean that Jenkins started as an anonymous user.
It just means that the person who started the build was not logged in. If you enable Jenkins security, you can create usernames for people and when they log in, the
"Started by anonymous"
will change to
"Started by < username >".
Note: You do not have to enable security in order to run jenkins or to clone correctly.
If you want to enable security and create users, you should see the options at Manage Jenkins > Configure System
.
ISSUE 2:
The "can't clone" error is a different issue altogether. It has nothing to do with you logging in to jenkins or enabling security. It just means that Jenkins does not have the credentials to clone from your git SCM.
Check out the Jenkins Git Plugin to see how to set up Jenkins to work with your git repository.
Hope that helps.