@Carolin Heyn,

Yes, I got it now😂😂, you need to write a trigger to get it done.

Before going to trigger, you need to create two things first.

1) Create a custom label with name "Auto Number" and give value = 0
2) Create a custom number field on Case object with label as "Auto Number"

once you do those two then create an apex class with name "AutoNumberonCase" and copy paste below code to your class.

public class AutoNumberonCase {
    //code by venkat for auto number on actionitem object for a build cycle
    public static void AutoNumber(List<Case> caseList){
        try{
            //Set to store the accountid from Case
            Set<Id> accountid = new Set<Id>();
            for(Case actionObj : caseList) {
                accountid.add(actionObj.AccountId);   
            }  
            
            //Fetch cases that are related to account
            List<Case> actionItemList2 = new List<Case>();
            actionItemList2 = [SELECT Id FROM Case WHERE AccountId IN :accountid]; 
            
            //Fetching cases in descending order to catch the highest Auto Number
            List<Account> accList = new List<Account>();
            accList = [SELECT Name, (SELECT Id, Auto_Number__c FROM Cases order by Auto_Number__c desc limit 1) FROM Account WHERE Id IN: accountid];
            
            for(Account bObj : accList){
                //custom label to assign first record to 1 if there are no existing records
                integer length = integer.valueOf(Label.Auto_Number);
               try{
                  //if auto number is not null for existing records then storing in inetger variable
               if(bObj.Cases[0].Auto_Number__c != null){
                    length = integer.valueOf(bObj.Cases[0].Auto_Number__c);
                    }
                }catch(exception e){
                }
                for(Case cObj : caseList){
                    if(bObj.Id == cObj.AccountId){
                            length++;
                            cObj.Auto_Number__c = length;
                    }
                }
                    
            }
       }catch(Exception e){
            System.debug('Exception in code'+e.getCause() + 'Exception in Line number'+e.getLineNumber());
       }
    }
}

then create a trigger on case object, copy paste below code.
 

trigger AutoNumber on Case (before insert) {
    if(trigger.isInsert && trigger.isBefore){
        AutoNumberonCase.AutoNumber(trigger.new);
    }

}

 then create a formula field on case object with return type as text and have below code in formula field.
 

LEFT( Account.Name,4) +"-" + TEXT(YEAR(TODAY())) +"-"+ TEXT(Auto_Number__c)

Mark it best if it solves your problem.