diff --git a/src/lightning/pytorch/CHANGELOG.md b/src/lightning/pytorch/CHANGELOG.md
index 9e6411cd7b..2a88d29f5b 100644
--- a/src/lightning/pytorch/CHANGELOG.md
+++ b/src/lightning/pytorch/CHANGELOG.md
@@ -50,6 +50,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Fixed automatic detection of 'last.ckpt' files to respect the extension when filtering ([#17072](https://github.com/Lightning-AI/lightning/pull/17072))
 
 
+- Fixed an issue where setting `CHECKPOINT_JOIN_CHAR` or `CHECKPOINT_EQUALS_CHAR` would only work on the `ModelCheckpoint` class but not on an instance ([#19054](https://github.com/Lightning-AI/lightning/pull/19054))
+
 
 ## [2.1.2] - 2023-11-15
 
diff --git a/src/lightning/pytorch/callbacks/model_checkpoint.py b/src/lightning/pytorch/callbacks/model_checkpoint.py
index f9c323f642..565aefaf3a 100644
--- a/src/lightning/pytorch/callbacks/model_checkpoint.py
+++ b/src/lightning/pytorch/callbacks/model_checkpoint.py
@@ -524,9 +524,8 @@ class ModelCheckpoint(Checkpoint):
 
         return should_update_best_and_save
 
-    @classmethod
     def _format_checkpoint_name(
-        cls,
+        self,
         filename: Optional[str],
         metrics: Dict[str, Tensor],
         prefix: str = "",
@@ -534,7 +533,7 @@ class ModelCheckpoint(Checkpoint):
     ) -> str:
         if not filename:
             # filename is not set, use default name
-            filename = "{epoch}" + cls.CHECKPOINT_JOIN_CHAR + "{step}"
+            filename = "{epoch}" + self.CHECKPOINT_JOIN_CHAR + "{step}"
 
         # check and parse user passed keys in the string
         groups = re.findall(r"(\{.*?)[:\}]", filename)
@@ -547,7 +546,7 @@ class ModelCheckpoint(Checkpoint):
             name = group[1:]
 
             if auto_insert_metric_name:
-                filename = filename.replace(group, name + cls.CHECKPOINT_EQUALS_CHAR + "{" + name)
+                filename = filename.replace(group, name + self.CHECKPOINT_EQUALS_CHAR + "{" + name)
 
             # support for dots: https://stackoverflow.com/a/7934969
             filename = filename.replace(group, f"{{0[{name}]")
@@ -557,7 +556,7 @@ class ModelCheckpoint(Checkpoint):
         filename = filename.format(metrics)
 
         if prefix:
-            filename = cls.CHECKPOINT_JOIN_CHAR.join([prefix, filename])
+            filename = self.CHECKPOINT_JOIN_CHAR.join([prefix, filename])
 
         return filename
 
diff --git a/tests/tests_pytorch/checkpointing/test_model_checkpoint.py b/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
index a7eb8b544a..81cc98cf50 100644
--- a/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
+++ b/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
@@ -402,34 +402,36 @@ def test_model_checkpoint_no_extraneous_invocations(tmpdir):
 
 
 def test_model_checkpoint_format_checkpoint_name(tmpdir, monkeypatch):
+    model_checkpoint = ModelCheckpoint(dirpath=tmpdir)
+
     # empty filename:
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("", {"epoch": 3, "step": 2})
+    ckpt_name = model_checkpoint._format_checkpoint_name("", {"epoch": 3, "step": 2})
     assert ckpt_name == "epoch=3-step=2"
 
-    ckpt_name = ModelCheckpoint._format_checkpoint_name(None, {"epoch": 3, "step": 2}, prefix="test")
+    ckpt_name = model_checkpoint._format_checkpoint_name(None, {"epoch": 3, "step": 2}, prefix="test")
     assert ckpt_name == "test-epoch=3-step=2"
 
     # no groups case:
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("ckpt", {}, prefix="test")
+    ckpt_name = model_checkpoint._format_checkpoint_name("ckpt", {}, prefix="test")
     assert ckpt_name == "test-ckpt"
 
     # no prefix
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("{epoch:03d}-{acc}", {"epoch": 3, "acc": 0.03})
+    ckpt_name = model_checkpoint._format_checkpoint_name("{epoch:03d}-{acc}", {"epoch": 3, "acc": 0.03})
     assert ckpt_name == "epoch=003-acc=0.03"
 
     # one metric name is substring of another
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("{epoch:03d}-{epoch_test:03d}", {"epoch": 3, "epoch_test": 3})
+    ckpt_name = model_checkpoint._format_checkpoint_name("{epoch:03d}-{epoch_test:03d}", {"epoch": 3, "epoch_test": 3})
     assert ckpt_name == "epoch=003-epoch_test=003"
 
     # prefix
-    monkeypatch.setattr(ModelCheckpoint, "CHECKPOINT_JOIN_CHAR", "@")
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("{epoch},{acc:.5f}", {"epoch": 3, "acc": 0.03}, prefix="test")
+    model_checkpoint.CHECKPOINT_JOIN_CHAR = "@"
+    ckpt_name = model_checkpoint._format_checkpoint_name("{epoch},{acc:.5f}", {"epoch": 3, "acc": 0.03}, prefix="test")
     assert ckpt_name == "test@epoch=3,acc=0.03000"
     monkeypatch.undo()
 
     # non-default char for equals sign
-    monkeypatch.setattr(ModelCheckpoint, "CHECKPOINT_EQUALS_CHAR", ":")
-    ckpt_name = ModelCheckpoint._format_checkpoint_name("{epoch:03d}-{acc}", {"epoch": 3, "acc": 0.03})
+    model_checkpoint.CHECKPOINT_EQUALS_CHAR = ":"
+    ckpt_name = model_checkpoint._format_checkpoint_name("{epoch:03d}-{acc}", {"epoch": 3, "acc": 0.03})
     assert ckpt_name == "epoch:003-acc:0.03"
     monkeypatch.undo()
 
@@ -454,13 +456,13 @@ def test_model_checkpoint_format_checkpoint_name(tmpdir, monkeypatch):
     assert ckpt_name == "epoch=4_val/loss=0.03000.ckpt"
 
     # auto_insert_metric_name=False
-    ckpt_name = ModelCheckpoint._format_checkpoint_name(
+    ckpt_name = model_checkpoint._format_checkpoint_name(
         "epoch={epoch:03d}-val_acc={val/acc}", {"epoch": 3, "val/acc": 0.03}, auto_insert_metric_name=False
     )
     assert ckpt_name == "epoch=003-val_acc=0.03"
 
     # dots in the metric name
-    ckpt_name = ModelCheckpoint._format_checkpoint_name(
+    ckpt_name = model_checkpoint._format_checkpoint_name(
         "mAP@0.50={val/mAP@0.50:.4f}", {"val/mAP@0.50": 0.2}, auto_insert_metric_name=False
     )
     assert ckpt_name == "mAP@0.50=0.2000"