diff --git a/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/mo_solve_nonhydro_4th_order_divdamp.py b/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/apply_4th_order_divergence_damping.py
similarity index 90%
rename from model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/mo_solve_nonhydro_4th_order_divdamp.py
rename to model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/apply_4th_order_divergence_damping.py
index 95570b6153..1bf79f880a 100644
--- a/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/mo_solve_nonhydro_4th_order_divdamp.py
+++ b/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/apply_4th_order_divergence_damping.py
@@ -20,11 +20,12 @@
 
 
 @field_operator
-def _mo_solve_nonhydro_4th_order_divdamp(
+def _apply_4th_order_divergence_damping(
     scal_divdamp: Field[[KDim], wpfloat],
     z_graddiv2_vn: Field[[EdgeDim, KDim], vpfloat],
     vn: Field[[EdgeDim, KDim], wpfloat],
 ) -> Field[[EdgeDim, KDim], wpfloat]:
+    '''Formelry known as _mo_solve_nonhydro_4th_order_divdamp.'''
     z_graddiv2_vn_wp = astype(z_graddiv2_vn, wpfloat)
     scal_divdamp = broadcast(scal_divdamp, (EdgeDim, KDim))
     vn_wp = vn + (scal_divdamp * z_graddiv2_vn_wp)
@@ -32,7 +33,7 @@ def _mo_solve_nonhydro_4th_order_divdamp(
 
 
 @program(grid_type=GridType.UNSTRUCTURED)
-def mo_solve_nonhydro_4th_order_divdamp(
+def apply_4th_order_divergence_damping(
     scal_divdamp: Field[[KDim], wpfloat],
     z_graddiv2_vn: Field[[EdgeDim, KDim], vpfloat],
     vn: Field[[EdgeDim, KDim], wpfloat],
@@ -41,7 +42,7 @@ def mo_solve_nonhydro_4th_order_divdamp(
     vertical_start: int32,
     vertical_end: int32,
 ):
-    _mo_solve_nonhydro_4th_order_divdamp(
+    _apply_4th_order_divergence_damping(
         scal_divdamp,
         z_graddiv2_vn,
         vn,
diff --git a/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/nh_solve/solve_nonhydro.py b/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/nh_solve/solve_nonhydro.py
index 256c35a984..5dc440917b 100644
--- a/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/nh_solve/solve_nonhydro.py
+++ b/model/atmosphere/dycore/src/icon4py/model/atmosphere/dycore/nh_solve/solve_nonhydro.py
@@ -85,8 +85,8 @@
 from icon4py.model.atmosphere.dycore.mo_math_gradients_grad_green_gauss_cell_dsl import (
     mo_math_gradients_grad_green_gauss_cell_dsl,
 )
-from icon4py.model.atmosphere.dycore.mo_solve_nonhydro_4th_order_divdamp import (
-    mo_solve_nonhydro_4th_order_divdamp,
+from icon4py.model.atmosphere.dycore.apply_4th_order_divergence_damping import (
+    apply_4th_order_divergence_damping,
 )
 from icon4py.model.atmosphere.dycore.add_analysis_increments_from_data_assimilation import (
     add_analysis_increments_from_data_assimilation,
@@ -1623,7 +1623,7 @@ def run_corrector_step(
                     )
                 else:
                     log.debug("corrector start stencil 4th order divdamp")
-                    mo_solve_nonhydro_4th_order_divdamp.with_backend(backend)(
+                    apply_4th_order_divergence_damping.with_backend(backend)(
                         scal_divdamp=self.scal_divdamp,
                         z_graddiv2_vn=self.z_graddiv2_vn,
                         vn=prognostic_state[nnew].vn,
diff --git a/model/atmosphere/dycore/tests/dycore_stencil_tests/test_mo_solve_nonhydro_4th_order_divdamp.py b/model/atmosphere/dycore/tests/dycore_stencil_tests/test_apply_4th_order_divergence_damping.py
similarity index 91%
rename from model/atmosphere/dycore/tests/dycore_stencil_tests/test_mo_solve_nonhydro_4th_order_divdamp.py
rename to model/atmosphere/dycore/tests/dycore_stencil_tests/test_apply_4th_order_divergence_damping.py
index c0fccfe30a..8a173ff7d0 100644
--- a/model/atmosphere/dycore/tests/dycore_stencil_tests/test_mo_solve_nonhydro_4th_order_divdamp.py
+++ b/model/atmosphere/dycore/tests/dycore_stencil_tests/test_apply_4th_order_divergence_damping.py
@@ -15,8 +15,8 @@
 import pytest
 from gt4py.next.ffront.fbuiltins import int32
 
-from icon4py.model.atmosphere.dycore.mo_solve_nonhydro_4th_order_divdamp import (
-    mo_solve_nonhydro_4th_order_divdamp,
+from icon4py.model.atmosphere.dycore.apply_4th_order_divergence_damping import (
+    apply_4th_order_divergence_damping,
 )
 from icon4py.model.common.dimension import EdgeDim, KDim
 from icon4py.model.common.test_utils.helpers import StencilTest, random_field
@@ -24,7 +24,7 @@
 
 
 class TestMoSolveNonhydro4thOrderDivdamp(StencilTest):
-    PROGRAM = mo_solve_nonhydro_4th_order_divdamp
+    PROGRAM = apply_4th_order_divergence_damping
     OUTPUTS = ("vn",)
 
     @staticmethod