diff --git a/pytorch_lightning/callbacks/model_checkpoint.py b/pytorch_lightning/callbacks/model_checkpoint.py
index 42c474e68c..44d586886a 100644
--- a/pytorch_lightning/callbacks/model_checkpoint.py
+++ b/pytorch_lightning/callbacks/model_checkpoint.py
@@ -498,7 +498,7 @@ class ModelCheckpoint(Callback):
 
     def _get_metric_interpolated_filepath_name(
         self,
-        monitor_candidates: Dict[str, Any],
+        ckpt_name_metrics: Dict[str, Any],
         epoch: int,
         step: int,
         trainer,
@@ -506,7 +506,7 @@ class ModelCheckpoint(Callback):
     ) -> str:
         filepath = self.format_checkpoint_name(epoch, step, ckpt_name_metrics)
 
-        version_cnt = 0
+        version_cnt = self.STARTING_VERSION
         while self.file_exists(filepath, trainer) and filepath != del_filepath:
             filepath = self.format_checkpoint_name(epoch, step, ckpt_name_metrics, ver=version_cnt)
             version_cnt += 1
@@ -518,7 +518,7 @@ class ModelCheckpoint(Callback):
         monitor_candidates.update(step=trainer.global_step, epoch=trainer.current_epoch)
         return monitor_candidates
 
-    def _save_last_checkpoint(self, trainer, pl_module, monitor_candidates):
+    def _save_last_checkpoint(self, trainer, pl_module, ckpt_name_metrics):
         should_save_last = self.monitor is None or self.save_last
         if not should_save_last:
             return
@@ -529,8 +529,8 @@ class ModelCheckpoint(Callback):
                 self.CHECKPOINT_NAME_LAST,
                 trainer.current_epoch,
                 trainer.global_step,
-                monitor_candidates,
-                prefix=self.prefix,
+                ckpt_name_metrics,
+                prefix=self.prefix
             )
             last_filepath = os.path.join(self.dirpath, f"{last_filepath}{self.FILE_EXTENSION}")
         else:
@@ -546,10 +546,10 @@ class ModelCheckpoint(Callback):
         else:
             self._save_model(last_filepath, trainer, pl_module)
         if (
-            self.last_model_path
-            and self.last_model_path != last_filepath
-            and (self.save_top_k != -1 or self.save_last)
-            and trainer.is_global_zero
+                self.last_model_path
+                and self.last_model_path != last_filepath
+                and (self.save_top_k != -1 or self.save_last)
+                and trainer.is_global_zero
         ):
             self._del_model(self.last_model_path)
         self.last_model_path = last_filepath