This assumes the name is for an object, where as the name could be from a modifier or a bone.

Instead namebutton_fn could call:

• WM_msg_publish_rna_prop(mbus, &ob->id, ob, Object, name);
• WM_msg_publish_rna_prop(mbus, &arm->id, ebone, EditBone, name);

and similar functions for other ID types, eventually this should replace the notifiers.

A larger refactor could use RNA, setting the "name" of each item, instead of having to add calls to BKE_object_defgroup_unique_name, BLI_libblock_ensure_unique_name.. etc, seems unnecessarily low level, for an operation RNA already supports.

The patch needs updating to apply on master.

• All the &tselem->id are passing the wrong pointer type, in most/all cases these have been assigned a variable, scene, object, armature etc. Those can be used instead.

source/blender/editors/space_outliner/outliner_draw.c:677:37: error: passing argument 1 of 'RNA_pointer_create' from incompatible pointer type [-Werror=incompatible-pointer-types]
  677 |       WM_msg_publish_rna_prop(mbus, &tselem->id, id, ID, name);
      |                                     ^~~~~~~~~~~
      |                                     |
      |                                     struct ID **

This also warns:

source/blender/editors/space_outliner/outliner_draw.c:733:11: error: a label can only be part of a statement and a declaration is not a statement
  733 |           bDeformGroup *vg = te->directdata;
      |           ^~~~~~~~~~~~