Field Update In contact name

try this below code....

trigger Sample_tri on Case (after insert) {
if(trigger.isInsert && trigger.isAfter){
   Map<ID,String>cids=new  Map<ID,String>();
   for(Case c:trigger.new){
     if(c.ContactId!=null && c.email__c!=null){
     String[] arrName =c.email__c.split('@');
     system.debug('--------'+arrName[1]);
     cids.put(c.ContactId,arrName[1]);
     }
   }
   List<Contact>ccc=[select id,lastname from Contact where id IN:cids.keySet()];
   for(contact c:ccc){
   c.lastName=cids.get(c.id);
   }
   update ccc;
}
}