GENERIC-FUNCTION-NAME is just a reader. The writer implements a different logic, acting via REINITIALIZE-INSTANCE.

src/clos/hierarchy.lsp

@@ -108,7 +108,7 @@
 (eval-when (:compile-toplevel :execute)
   (defparameter +standard-generic-function-slots+
     '((name :initarg :name :initform nil
-       :accessor generic-function-name)
+       :reader generic-function-name)
       (spec-list :initform nil :accessor generic-function-spec-list)
       (method-combination 
        :initarg :method-combination :initform (find-method-combination (class-prototype (find-class 'standard-generic-function)) 'standard nil)

src/clos/kernel.lsp

@@ -112,6 +112,11 @@
 	(setf (fdefinition name) gfun)
 	gfun)))
 
+(defun (setf generic-function-name) (new-name gf)
+  (if *clos-booted*
+      (reinitialize-instance gf :name new-name)
+      (setf (slot-value gf 'name) new-name)))
+
 (defun default-dispatch (generic-function)
   (cond ((null *clos-booted*)
 	 'standard-generic-function)

src/clos/method.lsp

@@ -374,7 +374,7 @@ have disappeared."
 ;;; early version used during bootstrap
 (defun add-method (gf method)
   (with-early-accessors (+standard-method-slots+ +standard-generic-function-slots+ +standard-class-slots+)
-    (let* ((name (generic-function-name gf))
+    (let* ((name (slot-value gf 'name))
 	   (method-entry (assoc name *early-methods*)))
       (unless method-entry
 	(setq method-entry (list name))