diff --git a/sklearn/metrics/_pairwise_distances_reduction/_argkmin.pyx.tp b/sklearn/metrics/_pairwise_distances_reduction/_argkmin.pyx.tp
index 1c1459e27f210..12746dcfbbeb3 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_argkmin.pyx.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_argkmin.pyx.tp
@@ -498,7 +498,7 @@ cdef class EuclideanArgKmin{{name_suffix}}(ArgKmin{{name_suffix}}):
             DTYPE_t squared_dist_i_j
             ITYPE_t n_X = X_end - X_start
             ITYPE_t n_Y = Y_end - Y_start
-            DTYPE_t * dist_middle_terms = self.gemm_term_computer._compute_distances_on_chunks(
+            DTYPE_t * dist_middle_terms = self.gemm_term_computer._compute_dist_middle_terms(
                 X_start, X_end, Y_start, Y_end, thread_num
             )
             DTYPE_t * heaps_r_distances = self.heaps_r_distances_chunks[thread_num]
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pxd.tp b/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pxd.tp
index 5978cfee9ebee..90a74374244ba 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pxd.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pxd.tp
@@ -76,7 +76,7 @@ cdef class GEMMTermComputer{{name_suffix}}:
         ITYPE_t thread_num
     ) nogil
 
-    cdef DTYPE_t * _compute_distances_on_chunks(
+    cdef DTYPE_t * _compute_dist_middle_terms(
         self,
         ITYPE_t X_start,
         ITYPE_t X_end,
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pyx.tp b/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pyx.tp
index 35e57219a96a7..cb44012a1c4b0 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pyx.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_gemm_term_computer.pyx.tp
@@ -32,10 +32,10 @@ from ...utils._cython_blas cimport (
 {{for name_suffix, upcast_to_float64, INPUT_DTYPE_t, INPUT_DTYPE in implementation_specific_values}}
 
 cdef class GEMMTermComputer{{name_suffix}}:
-    """Component for `FastEuclidean*` variant wrapping the logic for the call to GEMM.
+    """Component for `EuclideanDistance` specialisation wrapping the logic for the call to GEMM.
 
-    `FastEuclidean*` classes internally compute the squared Euclidean distances between
-    chunks of vectors X_c and Y_c using the following decomposition:
+    `EuclideanDistance` subclasses internally compute the squared Euclidean distances
+    between chunks of vectors X_c and Y_c using the following decomposition:
 
 
                 ||X_c_i - Y_c_j||² = ||X_c_i||² - 2 X_c_i.Y_c_j^T + ||Y_c_j||²
@@ -167,7 +167,7 @@ cdef class GEMMTermComputer{{name_suffix}}:
         return
 {{endif}}
 
-    cdef DTYPE_t * _compute_distances_on_chunks(
+    cdef DTYPE_t * _compute_dist_middle_terms(
         self,
         ITYPE_t X_start,
         ITYPE_t X_end,
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_radius_neighborhood.pyx.tp b/sklearn/metrics/_pairwise_distances_reduction/_radius_neighborhood.pyx.tp
index 8d50a6e04abf9..8c075482f2f6a 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_radius_neighborhood.pyx.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_radius_neighborhood.pyx.tp
@@ -506,7 +506,7 @@ cdef class EuclideanRadiusNeighbors{{name_suffix}}(RadiusNeighbors{{name_suffix}
             DTYPE_t squared_dist_i_j
             ITYPE_t n_X = X_end - X_start
             ITYPE_t n_Y = Y_end - Y_start
-            DTYPE_t *dist_middle_terms = self.gemm_term_computer._compute_distances_on_chunks(
+            DTYPE_t *dist_middle_terms = self.gemm_term_computer._compute_dist_middle_terms(
                 X_start, X_end, Y_start, Y_end, thread_num
             )