[SalesForce] How to insert object records using list of string

@Ashwani is right. You can put a where isConverted = false clause in the query for lead.

The existing code isn't too easy to follow. And with all the nested loops it's easy to imagine that duplicate items are getting added to a list. Rather than eliminating duplicates by using maps, I suggest it would be better to stop the code duplicating the data in the first place.

It is worth naming variables after their content and limiting their scope i.e. declare them where you need them and don't re-use them. The sort of code I would write for what I think you are doing (you may be doing something other than this so just take it as an example) is this:

   global void execute(
           Database.BatchableContext bc,
           List<Product_Metrics_vod__c> scope
           ) {
       // Find all keys
       Set<String> keys = new Set<String();
       for(Product_Metrics_vod__c pm : scope) {
           keys.add(key(pm));
       }
       // Query the existing ARs
       Map<String, Account_Report__c> keyToAr = new Map<String, Account_Report__c>();
       for (Account_Report__c ar : [
               SELECT Id, Name
               FROM Account_Report__c
               where Name IN :keys
               ]) {
           keyToAr.put(ar.Name, ar);
       }
       // Will update if already exists or will insert
       for (Product_Metrics_vod__c pm : scope) {
            Account_Report__c ar = keyToAr.get(key(pm));
            if (ar == null) {
                ar = new Account_Report__c(Name = key(pm));
                keyToAr.put(key(pm), ar);
            }
            ar.Account_Name__c = pm.Account_vod__c;
            ar.Product_Name__c = pm.Products_vod__c;
            ar.Loyalty__c = Integer.ValueOf(pm.Segment_Loyalty_LBK_FI__c);
            ar.Potential__c = pm.Segment_Potential_LBK_FI__c;
       }
       // Guaranteed only one value per key in this map
       upsert keyToAr.value();
   }
   private String key(Product_Metrics_vod__c pm) {
       return pm.Account_vod__c + '_' + pm.Products_vod__c;
   }

The above avoids multiple levels of loop nesting by using maps: this allows a value to be grabbed in a single statement rather than a set of values having to be looped over. Less code and execution time grows linearly rather than exponentially.