diff --git a/heudiconv/convert.py b/heudiconv/convert.py
index aecc70dc..c1fb1e39 100644
--- a/heudiconv/convert.py
+++ b/heudiconv/convert.py
@@ -523,6 +523,34 @@ def update_uncombined_name(
     return filename
 
 
+def update_multiorient_name(
+    metadata: dict[str, Any],
+    filename: str,
+) -> str:
+    if "acq-" in filename:
+        lgr.warning(
+            "Not embedding multi-orientation information as prefix already uses acq- parameter."
+        )
+        return filename
+    iop = metadata.get("ImageOrientationPatientDICOM")
+    iop = [round(x) for x in iop]
+    cross_prod = [
+        iop[1] * iop[5] - iop[2] * iop[4],
+        iop[2] * iop[3] - iop[0] * iop[5],
+        iop[0] * iop[4] - iop[1] * iop[3],
+    ]
+    cross_prod = [abs(x) for x in cross_prod]
+    slice_orient = ["sagittal", "coronal", "axial"][cross_prod.index(1)]
+    bids_pairs = filename.split("_")
+    # acq needs to be inserted right after sub- or ses-
+    ses_or_sub_idx = sum(
+        [bids_pair.split("-")[0] in ["sub", "ses"] for bids_pair in bids_pairs]
+    )
+    bids_pairs.insert(ses_or_sub_idx, "acq-%s" % slice_orient)
+    filename = "_".join(bids_pairs)
+    return filename
+
+
 def convert(
     items: list[tuple[str, tuple[str, ...], list[str]]],
     converter: str,
@@ -953,6 +981,7 @@ def save_converted_files(
         echo_times: set[float] = set()
         channel_names: set[str] = set()
         image_types: set[str] = set()
+        iops: set[str] = set()
         for metadata in bids_metas:
             if not metadata:
                 continue
@@ -968,6 +997,12 @@ def save_converted_files(
                 image_types.update(metadata["ImageType"])
             except KeyError:
                 pass
+            try:
+                iops.add(str(metadata["ImageOrientationPatientDICOM"]))
+            except KeyError:
+                pass
+
+        print(iops)
 
         is_multiecho = (
             len(set(filter(bool, echo_times))) > 1
@@ -978,6 +1013,7 @@ def save_converted_files(
         is_complex = (
             "M" in image_types and "P" in image_types
         )  # Determine if data are complex (magnitude + phase)
+        is_multiorient = len(iops) > 1
         echo_times_lst = sorted(echo_times)  # also converts to list
         channel_names_lst = sorted(channel_names)  # also converts to list
 
@@ -1008,6 +1044,11 @@ def save_converted_files(
                         bids_meta, this_prefix_basename, channel_names_lst
                     )
 
+                if is_multiorient:
+                    this_prefix_basename = update_multiorient_name(
+                        bids_meta, this_prefix_basename
+                    )
+
             # Fallback option:
             # If we have failed to modify this_prefix_basename, because it didn't fall
             #   into any of the options above, just add the suffix at the end:
diff --git a/heudiconv/tests/test_convert.py b/heudiconv/tests/test_convert.py
index ec63f4e2..0e39c269 100644
--- a/heudiconv/tests/test_convert.py
+++ b/heudiconv/tests/test_convert.py
@@ -17,6 +17,7 @@
     bvals_are_zero,
     update_complex_name,
     update_multiecho_name,
+    update_multiorient_name,
     update_uncombined_name,
 )
 from heudiconv.utils import load_heuristic
@@ -143,6 +144,18 @@ def test_update_uncombined_name() -> None:
         update_uncombined_name(metadata, base_fn, set(channel_names))  # type: ignore[arg-type]
 
 
+def test_update_multiorient_name() -> None:
+    """Unit testing for heudiconv.convert.update_multiorient_name(), which updates
+    filenames with the acq field if appropriate.
+    """
+    # Standard name update
+    base_fn = "sub-X_ses-Y_task-Z_run-01_bold"
+    metadata = {"ImageOrientationPatientDICOM": [0, 1, 0, 0, 0, -1]}
+    out_fn_true = "sub-X_ses-Y_acq-sagittal_task-Z_run-01_bold"
+    out_fn_test = update_multiorient_name(metadata, base_fn)
+    assert out_fn_test == out_fn_true
+
+
 def test_b0dwi_for_fmap(tmp_path: Path, caplog: pytest.LogCaptureFixture) -> None:
     """Make sure we raise a warning when .bvec and .bval files
     are present but the modality is not dwi.