[SalesForce] How does the field type “Auto Number” calculate

The value of auto_number__c is set when you insert the record. You would need to query the database to see what the value is.

For example

public PageReference MakeAnonymous(){
Account acc = new Account(Name='Anon');
insert acc;
acc = [select auto_number__c, name from account where id = :acc.id];
system.debug('account number..'+ acc.Auto_Number__c);
acc.Name = acc.Name + '-'+ acc.Auto_Number__c;
update acc;
}

It's a bit of a hack, but you could insert a record and immediately roll it back. That would give you the most recent auto-number, and you could increment it by 1 to figure out what the next probable number is. But like others have said, it's not guaranteed - for example, somebody else in the system could create a new record before the current user does, unit tests could run that insert these records, etc. Even the act of inserting a record and immediately rolling it back will cause the auto-number to increment (so therefore there will be at least one number separating any records created from this page).

CustomObject__c obj = new CustomObject__c();
Savepoint sp = Database.setSavepoint();
insert obj;
obj = [SELECT Name FROM CustomObject__c WHERE Id = :obj.Id];
System.debug(obj.Name); // This will be the current auto-number - increment it by one
Database.rollback(sp);

So, that's a solution you may be able to try if it's absolutely necessary to show the next probable number. I honestly wouldn't recommend it though, for the reasons stated above.