diff --git a/pytorch_lightning/callbacks/pruning.py b/pytorch_lightning/callbacks/pruning.py
index d3d280dbaa..ee130a700a 100644
--- a/pytorch_lightning/callbacks/pruning.py
+++ b/pytorch_lightning/callbacks/pruning.py
@@ -24,9 +24,10 @@ import torch
 import torch.nn.utils.prune as pytorch_prune
 from torch import nn
 
+from pytorch_lightning import _logger as log
 from pytorch_lightning.callbacks.base import Callback
 from pytorch_lightning.core.lightning import LightningModule
-from pytorch_lightning.utilities import rank_zero_info
+from pytorch_lightning.utilities import rank_zero_only
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 _PYTORCH_PRUNING_FUNCTIONS = {
@@ -152,6 +153,7 @@ class ModelPruning(Callback):
         self._parameter_names = parameter_names or self.PARAMETER_NAMES
         self._global_kwargs = {}
         self._original_layers = None
+        self._pruning_fn_name = None
 
         for name in self._parameter_names:
             if name not in self.PARAMETER_NAMES:
@@ -231,8 +233,14 @@ class ModelPruning(Callback):
         if self._use_global_unstructured:
             pruning_fn = _PYTORCH_PRUNING_METHOD[pruning_fn]
             self._global_kwargs = kwargs
+        else:
+            pruning_fn = _PYTORCH_PRUNING_FUNCTIONS[pruning_fn]
+        # save the function __name__ now because partial does not include it
+        # and there are issues setting the attribute manually in ddp.
+        self._pruning_fn_name = pruning_fn.__name__
+        if self._use_global_unstructured:
             return pruning_fn
-        return ModelPruning._wrap_pruning_fn(_PYTORCH_PRUNING_FUNCTIONS[pruning_fn], **kwargs)
+        return ModelPruning._wrap_pruning_fn(pruning_fn, **kwargs)
 
     @staticmethod
     def _wrap_pruning_fn(pruning_fn, **kwargs):
@@ -321,15 +329,15 @@ class ModelPruning(Callback):
             curr_stats = [self._get_pruned_stats(m, n) for m, n in self._parameters_to_prune]
             self._log_sparsity_stats(prev_stats, curr_stats, amount=amount)
 
+    @rank_zero_only
     def _log_sparsity_stats(
         self, prev: List[Tuple[int, int]], curr: List[Tuple[int, int]], amount: Union[int, float] = 0
     ):
         total_params = sum(p.numel() for layer, _ in self._parameters_to_prune for p in layer.parameters())
         prev_total_zeros = sum(zeros for zeros, _ in prev)
         curr_total_zeros = sum(zeros for zeros, _ in curr)
-        pruning_fn_name = self.pruning_fn.__name__
-        rank_zero_info(
-            f"Applied `{pruning_fn_name}`. Pruned:"
+        log.info(
+            f"Applied `{self._pruning_fn_name}`. Pruned:"
             f" {prev_total_zeros}/{total_params} ({prev_total_zeros / total_params:.2%}) ->"
             f" {curr_total_zeros}/{total_params} ({curr_total_zeros / total_params:.2%})"
         )
@@ -337,8 +345,8 @@ class ModelPruning(Callback):
             for i, (module, name) in enumerate(self._parameters_to_prune):
                 prev_mask_zeros, prev_mask_size = prev[i]
                 curr_mask_zeros, curr_mask_size = curr[i]
-                rank_zero_info(
-                    f"Applied `{pruning_fn_name}` to `{module!r}.{name}` with amount={amount}. Pruned:"
+                log.info(
+                    f"Applied `{self._pruning_fn_name}` to `{module!r}.{name}` with amount={amount}. Pruned:"
                     f" {prev_mask_zeros} ({prev_mask_zeros / prev_mask_size:.2%}) ->"
                     f" {curr_mask_zeros} ({curr_mask_zeros / curr_mask_size:.2%})"
                 )
diff --git a/tests/callbacks/test_pruning.py b/tests/callbacks/test_pruning.py
index 34fbd57203..62b0d3a8f3 100644
--- a/tests/callbacks/test_pruning.py
+++ b/tests/callbacks/test_pruning.py
@@ -76,7 +76,8 @@ def train_with_pruning_callback(
         "pruning_fn": pruning_fn,
         "amount": 0.3,
         "use_global_unstructured": use_global_unstructured,
-        "use_lottery_ticket_hypothesis": use_lottery_ticket_hypothesis
+        "use_lottery_ticket_hypothesis": use_lottery_ticket_hypothesis,
+        "verbose": 1,
     }
     if parameters_to_prune:
         pruning_kwargs["parameters_to_prune"] = [(model.layer.mlp_1, "weight"), (model.layer.mlp_2, "weight")]