diff --git a/src/anomalib/data/utils/synthetic.py b/src/anomalib/data/utils/synthetic.py
index 1726550f93..88e0a8707c 100644
--- a/src/anomalib/data/utils/synthetic.py
+++ b/src/anomalib/data/utils/synthetic.py
@@ -158,24 +158,26 @@ class SyntheticAnomalyDataset(AnomalibDataset):
         augmentations (Transform | None): Transform object describing the input data augmentations.
         source_samples: DataFrame containing normal samples used as source for
             synthetic anomalies.
+        dataset_name: str dataset name for path of temporary anomalous samples
 
     Example:
         >>> transform = Compose([...])
         >>> dataset = SyntheticAnomalyDataset(
         ...     transform=transform,
-        ...     source_samples=normal_df
+        ...     source_samples=normal_df,
+        ...     dataset_name="synthetic"
         ... )
         >>> len(dataset)  # 50/50 normal/anomalous split
         100
     """
 
-    def __init__(self, augmentations: Transform | None, source_samples: DataFrame) -> None:
+    def __init__(self, augmentations: Transform | None, source_samples: DataFrame, dataset_name: str) -> None:
         super().__init__(augmentations=augmentations)
 
         self.source_samples = source_samples
 
         # Files will be written to a temporary directory in the workdir
-        root = Path(ROOT)
+        root = Path(ROOT) / dataset_name
         root.mkdir(parents=True, exist_ok=True)
 
         self.root = Path(mkdtemp(dir=root))
@@ -194,6 +196,8 @@ def __init__(self, augmentations: Transform | None, source_samples: DataFrame) -
             0.5,
         )
 
+        self.samples.attrs["task"] = "segmentation"
+
     @classmethod
     def from_dataset(
         cls: type["SyntheticAnomalyDataset"],
@@ -212,7 +216,7 @@ def from_dataset(
             >>> normal_dataset = Dataset(...)
             >>> synthetic = SyntheticAnomalyDataset.from_dataset(normal_dataset)
         """
-        return cls(augmentations=dataset.augmentations, source_samples=dataset.samples)
+        return cls(augmentations=dataset.augmentations, source_samples=dataset.samples, dataset_name=dataset.name)
 
     def __copy__(self) -> "SyntheticAnomalyDataset":
         """Return shallow copy and prevent cleanup of original.
diff --git a/src/anomalib/utils/path.py b/src/anomalib/utils/path.py
index aea614eb54..7c8643e417 100644
--- a/src/anomalib/utils/path.py
+++ b/src/anomalib/utils/path.py
@@ -298,12 +298,10 @@ def generate_output_filename(
         >>> generate_output_filename(path, "/output", "MyDataset", "class_A")
         PosixPath('/output/image_001.jpg')
 
-        Dataset not found raises error:
+        Dataset not found returns the output path:
 
         >>> generate_output_filename("/wrong/path/image.png", "/out", "Missing")
-        Traceback (most recent call last):
-            ...
-        ValueError: Dataset name 'Missing' not found in the input path.
+        PosixPath('/out/wrong/path/image.png')
 
     Note:
         - Directory structure after ``dataset_name`` (or ``category`` if provided) is
@@ -315,12 +313,12 @@ def generate_output_filename(
     input_path = Path(input_path)
     output_path = Path(output_path)
 
-    # Find the position of the dataset name in the path
-    try:
+    # Check if the dataset name is in the input path. If not, just use the output path
+    if dataset_name.lower() not in [x.lower() for x in input_path.parts]:
+        dataset_index = len(input_path.parts)
+    else:
+        # Find the position of the dataset name in the path
         dataset_index = next(i for i, part in enumerate(input_path.parts) if part.lower() == dataset_name.lower())
-    except ValueError:
-        msg = f"Dataset name '{dataset_name}' not found in the input path."
-        raise ValueError(msg) from None
 
     # Determine the start index for preserving subdirectories
     start_index = dataset_index + 1
diff --git a/tests/unit/data/utils/test_synthetic.py b/tests/unit/data/utils/test_synthetic.py
index 5bab62f0a9..90360078c8 100644
--- a/tests/unit/data/utils/test_synthetic.py
+++ b/tests/unit/data/utils/test_synthetic.py
@@ -40,6 +40,7 @@ def synthetic_dataset_from_samples(folder_dataset: FolderDataset) -> SyntheticAn
     return SyntheticAnomalyDataset(
         augmentations=folder_dataset.augmentations,
         source_samples=folder_dataset.samples,
+        dataset_name=folder_dataset.name,
     )