SQL Server 2008 - is "NT AUTHORITY\ANONYMOUS LOGON" login "mandatory"?
This account seems to allow login for every people that are in my domain


That is actually incorrect. It allows access to anyone that cannot be authenticated. Members of your domains will successfully authenticate and they will be rejected.

On a serious note: there is absolutely ZERO reasons to have this login enabled. It was added intentionally to your system by somebody, this is not a default configuration. If I'd venture a guess, it would be that somebody tried to configure integrated authentication with impersonation on a web application and did not understand the requirement for 'double hop' constrained delegation. Needless to say, the 'solution' is a huge security hole that requires immediate action. You need to identify the application that uses this login and fix the authentication as appropriate (the link contains the primer on how to set up constrained delegation).