diff --git a/train_model.py b/train_model.py
index be4f25f9..8ecc148b 100644
--- a/train_model.py
+++ b/train_model.py
@@ -1,3 +1,4 @@
+import random
 import torch
 import pytorch_lightning as pl
 from lightning_fabric.utilities import seed
@@ -82,6 +83,9 @@ def main():
     assert args.step_length <= 3, "Too high step length"
     assert args.eval in (None, "val", "test"), f"Unknown eval setting: {args.eval}"
 
+    # Get an (actual) random run id as a unique identifier
+    random_run_id = random.randint(0, 9999)
+
     # Set seed
     seed.seed_everything(args.seed)
 
@@ -120,7 +124,7 @@ def main():
     if args.eval:
         prefix = prefix + f"eval-{args.eval}-"
     run_name = f"{prefix}{args.model}-{args.processor_layers}x{args.hidden_dim}-"\
-        f"{time.strftime('%m_%d_%H_%M_%S')}"
+            f"{time.strftime('%m_%d_%H')}-{random_run_id:04d}"
     checkpoint_callback = pl.callbacks.ModelCheckpoint(
             dirpath=f"saved_models/{run_name}", filename="min_val_loss",
             monitor="val_mean_loss", mode="min", save_last=True)