Adding 'NT AUTHORITY\ANONYMOUS LOGON' would have to be pretty close to the top of the list of BAD practises. I strongly recommend that you delete these logins. Whilst they might be valid users, they may well be attempts to access your server without any valid reason/credentials.

If they happen to be valid attempts to login to the server, you really need to determine why this is happening and correct the issue so that valid credentials are used. It may be that, for instance, Kerberos authentication is not correctly configured on one of your servers. Fixing that would be the correct action to take (instead of adding 'NT AUTHORITY\ANONYMOUS LOGON' to your server)