diff --git a/scripts/addons_core/io_anim_bvh/import_bvh.py b/scripts/addons_core/io_anim_bvh/import_bvh.py
index 5f3872a28cf..f999eece177 100644
--- a/scripts/addons_core/io_anim_bvh/import_bvh.py
+++ b/scripts/addons_core/io_anim_bvh/import_bvh.py
@@ -518,7 +518,13 @@ def bvh_node_dict2armature(
 
     arm_ob_adt = arm_ob.animation_data_create()
     action = bpy.data.actions.new(name=bvh_name)
-    action_slot = action.slots.new(arm_ob.id_type, arm_ob.name)
+    # Always use the same name for the slot. The Armature is named after the
+    # BVH file, and so when importing multiple files to get multiple Actions
+    # for a single character, it is likely that all but one of the Armatures
+    # is going to be deleted again. It should be simple to switch between
+    # imported Actions while keeping Slot auto-assignment, which means that
+    # all Actions should use the same slot name.
+    action_slot = action.slots.new(arm_ob.id_type, "Slot")
 
     arm_ob_adt.action = action
     arm_ob_adt.action_slot = action_slot
diff --git a/scripts/addons_core/io_scene_fbx/import_fbx.py b/scripts/addons_core/io_scene_fbx/import_fbx.py
index 9f688620b37..e86a781527d 100644
--- a/scripts/addons_core/io_scene_fbx/import_fbx.py
+++ b/scripts/addons_core/io_scene_fbx/import_fbx.py
@@ -1098,8 +1098,14 @@ def blen_read_animations(fbx_tmpl_astack, fbx_tmpl_alayer, stacks, scene, anim_o
                     actions[key] = action = bpy.data.actions.new(action_name)
                     action.use_fake_user = True
 
-                    # Create an Action Slot. Curves created via action.fcurves will automatically be assigned to it.
-                    action.slots.new(id_data.id_type, action_name)
+                    # Always use the same name for the slot. It should be simple
+                    # to switch between imported Actions while keeping Slot
+                    # auto-assignment, which means that all Actions should use
+                    # the same slot name. As long as there's no separate
+                    # indicator for the "intended object name" for this FBX
+                    # animation, this is the best Blender can do. Maybe the
+                    # 'stack name' would be a better choice?
+                    action.slots.new(id_data.id_type, "Slot")
 
                 # If none yet assigned, assign this action to id_data.
                 if not id_data.animation_data: